I think the best answer to this is to let the Bible speak for itself. For we can see clearly what the Lord would have us do when faced with someone that is of a contentious nature. Here is what we found:

Thou shalt not go up and down as a talebearer among thy people: neither shalt thou stand against the blood of thy neighbour: I am the Lord. Leviticus 19:16

Thou shalt not avenge, nor bear any grudge against the children of thy people, but thou shalt love thy neighbour as thyself: I am the Lord. Leviticus 19:18

But the stranger that dwelleth with you shall be unto you as one born among you, and thou shalt love him as thyself; for ye were strangers in the land of Egypt: I am the Lord your God. Leviticus 19:34

Love ye therefore the stranger: for ye were strangers in the land of Egypt. Deut. 10:19

The Lord shall cut off all flattering lips, and the tongue that speaketh proud things: Who have said, With our tongue will we prevail; our lips are our own: who is lord over us? Psalm 12:3-4

Cease from anger, and forsake wrath: fret not thyself in any wise to do evil. Psalm 37:8

They compassed me about also with words of hatred; and fought against me without a cause. For my love they are my adversaries: but I give myself unto prayer. Psalm 109:3-4

Great peace have they which love thy law: and nothing shall offend them. Psalm 119:165

Devise not evil against thy neighbour, seeing he dwelleth securely by thee. Strive not with a man without cause, if he have done thee no harm. Proverbs 3:29-30

Hatred stirreth up strifes: but love covereth all sins. Proverbs 10:12

An hypocrite with his mouth destroyeth his neighbour: but through knowledge shall the just be delivered. Proverbs 11:9

He that is void of wisdom despiseth his neighbour: but a man of understanding holdeth his peace. Proverbs 11:12

Only by pride cometh contention: but with the well advised is wisdom. Proverbs 13:10

He that despiseth his neighbour sinneth: but he that hath mercy on the poor, happy is he. Proverbs 14:21

A soft answer turneth away wrath: but grievous words stir up anger. Proverbs 15:1

A wrathful man stirreth up strife: but he that is slow to anger appeaseth strife. Proverbs 15:18

Better is a dry morsel, and quietness therewith, than an house full of sacrifices with strife. Proverbs 17:1

The beginning of strife is as when one letteth out water: therefore leave off contention, before it be meddled with. Proverbs 17:14

He loveth transgression that loveth strife: and he that exalteth his gate seeketh destruction. Proverbs 17:19

A fool's lips enter into contention, and his mouth calleth for strokes. A fool's mouth is his destruction, and his lips are the snare of his soul. The words of a talebearer are as wounds, and they go down into the innermost parts of the belly. Proverbs 18:6-8

A brother offended is harder to be won than a strong city: and their contentions are like the bars of a castle. Proverbs 18:19

It is an honour for a man to cease from strife: but every fool will be meddling. Proverbs 20:3

Cast out the scorner, and contention shall go out; yea, strife and reproach shall cease. Proverbs 22:10

Debate thy cause with thy neighbour himself; and discover not a secret to another: Proverbs 25:9

If thine enemy be hungry, give him bread to eat; and if he be thirsty, give him water to drink: For thou shalt heap coals of fire upon his head, and the Lord shall reward thee. Proverbs 25:21-22

He that passeth by, and meddleth with strife belonging not to him, is like one that taketh a dog by the ears. Proverbs 26:17

Where no wood is, there the fire goeth out: so where there is no talebearer, the strife ceaseth. Proverbs 26:20

As coals are to burning coals, and wood to fire; so is a contentious man to kindle strife. Proverbs 26:21

He that is of a proud heart stirreth up strife: but he that putteth his trust in the Lord shall be made fat. Proverbs 28:25

An angry man stirreth up strife, and a furious man aboundeth in transgression. Proverbs 29:22

Behold, ye fast for strife and debate, and to smite with the fist of wickedness: ye shall not fast as ye do this day, to make your voice to be heard on high. Is it such a fast that I have chosen? a day for a man to afflict his soul? is it to bow down his head as a bulrush, and to spread sackcloth and ashes under him? wilt thou call this a fast, and an acceptable day to the Lord? Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke? Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?

Then shall thy light break forth as the morning, and thine health shall spring forth speedily: and thy righteousness shall go before thee; the glory of the Lord shall be thy rereward. Then shalt thou call, and the Lord shall answer; thou shalt cry, and he shall say, Here I am. If thou take away from the midst of thee the yoke, the putting forth of the finger, and speaking vanity; And if thou draw out thy soul to the hungry, and satisfy the afflicted soul; then shall thy light rise in obscurity, and thy darkness be as the noonday: And the Lord shall guide thee continually, and satisfy thy soul in drought, and make fat thy bones: and thou shalt be like a watered garden, and like a spring of water, whose waters fail not. Isaiah 58:4-11

But let your communication be, Yea, yea; Nay, nay: for whatsoever is more than these cometh of evil. Matthew 5:37

But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you; That ye may be the children of your Father which is in heaven: for he maketh his sun to rise on the evil and on the good, and sendeth rain on the just and on the unjust. For if ye love them which love you, what reward have ye? do not even the publicans the same? And if ye salute your brethren only, what do ye more than others? do not even the publicans so? Be ye therefore perfect, even as your Father which is in heaven is perfect. Matthew 5:44-48

Judge not, that ye be not judged. For with what judgment ye judge, ye shall be judged: and with what measure ye mete, it shall be measured to you again. And why beholdest thou the mote that is in thy brother's eye, but considerest not the beam that is in thine own eye? Or how wilt thou say to thy brother, Let me pull out the mote out of thine eye; and, behold, a beam is in thine own eye? Thou hypocrite, first cast out the beam out of thine own eye; and then shalt thou see clearly to cast out the mote out of thy brother's eye. Matthew 7:1-5

Therefore all things whatsoever ye would that men should do to you, do ye even so to them: for this is the law and the prophets. Matthew 7:12

And whosoever shall not receive you, nor hear your words, when ye depart out of that house or city, shake off the dust of your feet. Verily I say unto you, It shall be more tolerable for the land of Sodom and Gomorrha in the day of judgment, than for that city. Behold, I send you forth as sheep in the midst of wolves: be ye therefore wise as serpents, and harmless as doves. Matthew 10:14-16

Moreover if thy brother shall trespass against thee, go and tell him his fault between thee and him alone: if he shall hear thee, thou hast gained thy brother. But if he will not hear thee, then take with thee one or two more, that in the mouth of two or three witnesses every word may be established. And if he shall neglect to hear them, tell it unto the church: but if he neglect to hear the church, let him be unto thee as an heathen man and a publican. Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven. Matthew 18:15-18

But Jesus called them unto him, and said, Ye know that the princes of the Gentiles exercise dominion over them, and they that are great exercise authority upon them. But it shall not be so among you: but whosoever will be great among you, let him be your minister; And whosoever will be chief among you, let him be your servant: Even as the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many. Matthew 20:25-28

But he that is greatest among you shall be your servant. And whosoever shall exalt himself shall be abased; and he that shall humble himself shall be exalted. Matthew 23:11-12

And the high priest arose, and said unto him, Answerest thou nothing? what is it which these witness against thee? But Jesus held his peace. And the high priest answered and said unto him, I adjure thee by the living God, that thou tell us whether thou be the Christ, the Son of God. Jesus saith unto him, Thou hast said: nevertheless I say unto you, Hereafter shall ye see the Son of man sitting on the right hand of power, and coming in the clouds of heaven. Then the high priest rent his clothes, saying, He hath spoken blasphemy; what further need have we of witnesses? behold, now ye have heard his blasphemy. What think ye? They answered and said, He is guilty of death. Then did they spit in his face, and buffeted him; and others smote him with the palms of their hands, Saying, Prophesy unto us, thou Christ, Who is he that smote thee? Matthew 26:62-68

And Jesus stood before the governor: and the governor asked him, saying, Art thou the King of the Jews? And Jesus said unto him, Thou sayest. And when he was accused of the chief priests and elders, he answered nothing. Then said Pilate unto him, Hearest thou not how many things they witness against thee? And he answered him to never a word; insomuch that the governor marvelled greatly. Matthew 27:11-14

But I say unto you which hear, Love your enemies, do good to them which hate you, Bless them that curse you, and pray for them which despitefully use you. Luke 6:27-28

And there was also a strife among them, which of them should be accounted the greatest. And he said unto them, The kings of the Gentiles exercise lordship over them; and they that exercise authority upon them are called benefactors. But ye shall not be so: but he that is greatest among you, let him be as the younger; and he that is chief, as he that doth serve. For whether is greater, he that sitteth at meat, or he that serveth? is not he that sitteth at meat? but I am among you as he that serveth. Luke 22:24-27

Be kindly affectioned one to another with brotherly love; in honour preferring one another; Romans 12:10

If it be possible, as much as lieth in you, live peaceably with all men. Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord. Therefore if thine enemy hunger, feed him; if he thirst, give him drink: for in so doing thou shalt heap coals of fire on his head. Be not overcome of evil, but overcome evil with good. Romans 12:18-21

Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness, Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies, Envyings, murders, drunkenness, revellings, and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God. But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith, Meekness, temperance: against such there is no law. And they that are Christ's have crucified the flesh with the affections and lusts. Galatians 5:19-24

Let nothing be done through strife or vainglory; but in lowliness of mind let each esteem other better than themselves. Look not every man on his own things, but every man also on the things of others. Let this mind be in you, which was also in Christ Jesus: Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men: And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross. Philip. 2:3-8

See that none render evil for evil unto any man; but ever follow that which is good, both among yourselves, and to all men. 1 Thes. 5:15

If any man teach otherwise, and consent not to wholesome words, even the words of our Lord Jesus Christ, and to the doctrine which is according to godliness; He is proud, knowing nothing, but doting about questions and strifes of words, whereof cometh envy, strife, railings, evil surmisings, Perverse disputings of men of corrupt minds, and destitute of the truth, supposing that gain is godliness: from such withdraw thyself. But godliness with contentment is great gain. 1 Tim. 6:3-6

But if ye have bitter envying and strife in your hearts, glory not, and lie not against the truth. This wisdom descendeth not from above, but is earthly, sensual, devilish. For where envying and strife is, there is confusion and every evil work. But the wisdom that is from above is first pure, then peaceable, gentle, and easy to be intreated, full of mercy and good fruits, without partiality, and without hypocrisy. James 3:14-17

Now after reading those what should we do? Do we go out and argue with those not of our faith that disagree with us? No, we are not to force our beliefs on another person. In Zechariah 4:6 we are told that it is "not by might, nor by power, but by my spirit, saith the Lord of hosts." Some say that we are to "contend for the faith" but was Jude talking about being contentious? I don’t think so, not with the weight of evidence here given from the rest of the Bible. But some seem to think that that is the only way to deal with people not of their faith. In Acts 9 we find how Saul treated people that didn’t believe the way he thought they should. But in verses 4-5 we find what Christ said to him:

And he fell to the earth, and heard a voice saying unto him, Saul, Saul, why persecutest thou me? And he said, Who art thou, Lord? And the Lord said, I am Jesus whom thou persecutest: it is hard for thee to kick against the pricks. Acts 9:4-5

Christ before his death and resurrection had said this:

And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me. Matthew 25:40

But he, willing to justify himself, said unto Jesus, And who is my neighbour? And Jesus answering said, A certain man went down from Jerusalem to Jericho, and fell among thieves, which stripped him of his raiment, and wounded him, and departed, leaving him half dead. And by chance there came down a certain priest that way: and when he saw him, he passed by on the other side. And likewise a Levite, when he was at the place, came and looked on him, and passed by on the other side. But a certain Samaritan, as he journeyed, came where he was: and when he saw him, he had compassion on him, And went to him, and bound up his wounds, pouring in oil and wine, and set him on his own beast, and brought him to an inn, and took care of him. And on the morrow when he departed, he took out two pence, and gave them to the host, and said unto him, Take care of him; and whatsoever thou spendest more, when I come again, I will repay thee. Which now of these three, thinkest thou, was neighbour unto him that fell among the thieves? And he said, He that shewed mercy on him. Then said Jesus unto him, Go, and do thou likewise. Luke 10:29-37

You may ask "Should we play sports?" I don’t see how we could, and still call ourselves Christian. A real Christian will be like Christ, serving others not fighting against them. How many "Christian" athletic teams would want to have you on their team if you took the counsel seriously found in Romans 12:10 to "be kindly affectioned one to another with brotherly love; in honour prefering one another"? If you truly prefer the other person as we are told to in the Bible you would be helping the other team win. You would not want to see them loose or be hurt. Ask yourself this: "Do sports fit what you find in Philippians 4:8?", which says:

Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report; if there be any virtue, and if there be any praise, think on these things. Philip. 4:8

Some may say that sports is not for real it is just play. But what does the Bible say:

Incline not my heart to any evil thing, to practise wicked works with men that work iniquity: and let me not eat of their dainties. Psalm 141:4

What about just watching the games.

I will set no wicked thing before mine eyes: I hate the work of them that turn aside; it shall not cleave to me. Psalm 101:3

Why should someone give these things up? Is it of a life and death issue?

Better it is to be of an humble spirit with the lowly, than to divide the spoil with the proud. Proverbs 16:19

But the meek shall inherit the earth; and shall delight themselves in the abundance of peace. Psalm 37:11

The Lord lifteth up the meek: he casteth the wicked down to the ground. Psalm 147:6

For the Lord taketh pleasure in his people: he will beautify the meek with salvation. Psalm 149:4

The Spirit of the Lord God is upon me; because the Lord hath anointed me to preach good tidings unto the meek; he hath sent me to bind up the brokenhearted, to proclaim liberty to the captives, and the opening of the prison to them that are bound; Isaiah 61:1

Some excuse themselves because God told the people of Israel to kill the people of Canaan but the Bible says:

And I will send hornets before thee, which shall drive out the Hivite, the Canaanite, and the Hittite, from before thee. Exodus 23:28

And I will send an angel before thee; and I will drive out the Canaanite, the Amorite, and the Hittite, and the Perizzite, the Hivite, and the Jebusite: Exodus 33:2