The Bible has made plain several viewpoints. The famous 'do not yoke' passage does not apply to marital relationships but also to relationships whereby both parties need a certain common ground of understanding. For instance, Business partners.
One cannot see this biblical teaching as Isolation from the world, infact the Bible promotes holy worldliness. That is to say, be IN the world but not OF the world. Jesus, being the sinless Son of God did not shun Himself away from sinners. On the contrary, the fact that He often mingles with tax collectors and harlots caused the religious leaders of His days to see Him as being revoluntionary. Christians are called to be the salt and light in the world living in darkness and not to light up a lamp and place it under a bowl as the gospel parable described.
However, as much as Christians should mingle with people of different faith. there must be a clear distinction between those of God and those who are otherwise. The Bible often provides us with examples whereby consecration to God and being owned by God is one important identity in Christ. not denominations, sectarian differences. Salvation through Christ by grace and through faith alone is what mark a believer from a non-believer. Because of this tremendous change in spiritual status of a person, there must also be physical adjustments being made. Water Baptism and Lord's supper are two main outward signs of an inward grace.
Marriage has a special place in the heart of God. Adam and Eve was a classic example where God for the first time ordain marriage. And part of this covenant is the physical union between a male and a female which results in offsprings being produced which populates the entire world. Which God said be fruitful and multiply. Sexual union is not merely the fusion of a sperm and an egg, in the biblical context, sexual union involves spiritual union as well. And it is because of this aspect particularly the bible forbades uniting things of God with things of the devil (that is to say, of the world). These 2 are not the same, they do not agree with each other and infact are in perpetual conflict.
More than religious differences between a Christian and a non-Christian, some people say that even in such circumstances, true love exists..which is in every way possible. But as a Christian, we are not just called to love our spouses and produce children and start a family under the context of marriage but more importantly, for any Bible-believing and God-loving individual to serve God and honour Him in every manner of his/her life. That require total surrender of one's life to God Most High and with that deny everything that obstruct him/her from pursuing this greatest call in the christian journey. Such a thing cannot be made fully possible unless both parties share the same spiritual heritage and call upon the same God. If not, very often the Christian party will be influenced and eventually give up in his/her spiritual pursuits. There is no such thing as 'evangelistic marriage'
On the other hand, having said about the above. In
1 Peter 3:1-7, we see an example of a non-believing man and a believer wife. However, in this context it is because the wives came to know the Lord after their marriage. And we should take good notice that the Scripture never in any way suggest a divorce. Therefore, this whole issue of unequally yoked relationship should be understood and appreciate in the context of the God's Word which always seeks the common good of all who read it and intend to build up things that are pure and good, while demolishing all that are guilty and full of evil intents.