We have to deal with the world's system and those in it, but we need to be careful and maintain proper balance. We should avoid relationships with those who influence us negatively more than we influence them positively.
Marriage is one area where this principle is especially true. There is no closer union in life than the marriage relationship. A believer who marries an unbeliever is directly violating this scripture and is messing with disaster. The Lord should be the most important person in our life. How could we possibly become "one" with a person who doesn't love our Lord?
It is foolish to think that after marriage an unbelieving spouse will accept the Lord. It has happened, but it cannot be guaranteed. In fact, statistics are overwhelmingly against this happening. Regardless of that possibility, a believer who marries an unbeliever is directly violating God's instructions here. It is not a good start to any marriage to reject God's Word.
Being unequally yoked with unbelievers just doesn't work. Believers and unbelievers are as different as righteousness and unrighteousness, light and dark, Christ and the devil. One has faith and the other has none. One is the temple of God and the other an idol. Any Christian who doesn't see this conflict is deceived.