How should Christians act toward non-Christians?
One example I have found is 2 Corinthians 6:14 [KJV].
Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
I believe this is saying not to marry non-Christians.
Are there any other instructions on how to behave towards non-Christians in the Bible?
They are our neighbors and we should love them as ourselves.
34 “A new command I give you: Love one another. As I have loved you, so you must love one another. 35 By this everyone will know that you are my disciples, if you love one another.”
If it turns out that they are our enemies then we should love them all them more.
Matthew 5:43-44 (NIV)
43 “You have heard that it was said, ‘Love your neighbor and hate your enemy.’ 44 But I tell you, love your enemies and pray for those who persecute you,
You're right, from a strictly Biblical perspective, marriage to non-Christians should be off the table. Personally, I've even witnessed relationships between denominations deteriorate due to theological differences, but in an inter-religion marriage there can be some serious issues -- either faith is watered down, or it is a source of contention.
We are also cautioned not to give that which is holy to those who are not baptized:
Give not that which is holy to dogs; neither cast ye your pearls before swine, lest perhaps they trample them under their feet, and turning upon you, they tear you. (Mat. 7:6)
The ancient Church (the Catholics only ended this recently and my understanding is that the Orthodox continue to do this to today) took this to mean that the outsider was welcome through the preaching and recitation and exposition on the religious texts, but that the holy meal was reserved to the initiated (read up on mystagogy for good stuff on this)
Some can be read into the admonitions related to what later became excommunication. Here is a pertinent text about those who have fallen into habitual (in this case sexual) immorality:
To deliver such a one to Satan for the destruction of the flesh, that the spirit may be saved in the day of our Lord Jesus Christ.(1 Cor. 5:13)
And, according to the Johannine texts these should not be considered part of the congregation:
Whosoever revolteth and continueth not in the doctrine of Christ hath not God. (2 John 9)
That said the story of the Good Samaritan would suggest that love crosses all bounds (and if you want a fascinating history, read about Israel, Judah, and the origin of the Samaritans). Further, the Old Testament is full of admonitions to defend the foreigners:
If a stranger dwell in your land, and abide among you, do not upbraid hin: But let him be among you as one of the same country. And you shall love him as yourselves: for you were strangers in the land of Egypt. I am the Lord your God. (Lev. 19:33-34)
It seems, all considered, that the admonition to love (cf. Mt. 7:12, Lk. 6:31) is universal and should be universally applied, but the alien is still an alien. It is fine to fellowship with those in the world, but spiritual communion should be reserved to those who are among the flock.
The way Jesus treated each and every one of the people he encountered; with love, compassion and mercy.
It's all there in the Gospels and Paul's letters to the churches, Jesus is who we should aim to emulate.
In addition to the [obvious] exclusion of marriage, it would seem to indicate (in my understanding) that we should not become unduly-bound to an unbeliever in other relationships, as well.
It is [likely] impossible for one to only work with and for another christian. However, intentionally going into business with an unbeliever could be considered an unequal yoking.
Paul taught Timothy,
"Let no man despise thy youth; but be thou an example of the believers, in word, in conversation, in charity, in spirit, in faith, in purity." (1 Timothy 4:12)
So obviously we are to be an example to the unbelievers of what a believer is. By the way we talk, what we talk about, how we treat others, by the way we pray, how we exercise our faith in God, in how we live a pure life.
Jesus taught from the Sermon on the Mount,
3 Blessed are the poor in spirit: for theirs is the kingdom of heaven.
4 Blessed are they that mourn: for they shall be comforted.
5 Blessed are the meek: for they shall inherit the earth.
6 Blessed are they which do hunger and thirst after righteousness: for they shall be filled.
7 Blessed are the merciful: for they shall obtain mercy.
8 Blessed are the pure in heart: for they shall see God.
9 Blessed are the peacemakers: for they shall be called the children of God.
10 Blessed are they which are persecuted for righteousness’ sake: for theirs is the kingdom of heaven.
11 Blessed are ye, when men shall revile you, and persecute you, and shall say all manner of evil against you falsely, for my sake.
12 Rejoice, and be exceeding glad: for great is your reward in heaven: for so persecuted they the prophets which were before you.
13 Ye are the salt of the earth: but if the salt have lost his savour, wherewith shall it be salted? it is thenceforth good for nothing, but to be cast out, and to be trodden under foot of men.
14 Ye are the alight of the world. A city that is set on an hill cannot be hid.
15 Neither do men light a candle, and put it under a bushel, but on a candlestick; and it giveth light unto all that are in the house.
16 Let your alight so shine before men, that they may see your good works, and glorify your Father which is in heaven." (Matthew 5:13)
If I understand what Jesus is saying, He is telling us to mourn with those who mourn, visit the sick and imprisoned, be a light, a city on a hill, the salt of the earth to give flavor to the community.
Jesus once was asked, "Who is my neighbor?" Upon which, the Lord gave the parable of the Good Samaritan and then asked again,
"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)
