The passage of scripture usually cited against interracial marriage is Deuteronomy 7:1-4:
When the LORD thy God shall bring thee into the land whither thou goest to possess it, and hath cast out many nations before thee, the Hittites, and the Girgashites, and the Amorites, and the Canaanites, and the Perizzites, and the Hivites, and the Jebusites, seven nations greater and mightier than thou;
And when the LORD thy God shall deliver them before thee; thou shalt smite them, and utterly destroy them; thou shalt make no covenant with them, nor shew mercy unto them:
Neither shalt thou make marriages with them; thy daughter thou shalt not give unto his son, nor his daughter shalt thou take unto thy son.
For they will turn away thy son from following me, that they may serve other gods: so will the anger of the LORD be kindled against you, and destroy thee suddenly.
The reader will notice that the prohibition was against having friendly relations with seven specific nations because they followed other gods, not because their skin was a different colour. It’s also stated that these seven nations were greater and mightier than Israel; if Israel were to make covenants with and intermarry with these nations, the likely result would be that Israel would be overwhelmed and absorbed by them, and would lose her distinct identity, which was definitely not part of God's plan. None of the reasons against intermarriage cited in the passage above are applicable to Bob Jones University.
The New Testament passage most frequently cited against marrying unbelievers is II Corinthians 6:14-17:
Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
And what concord hath Christ with Belial? or what part hath he that believeth with an infidel?
And what agreement hath the temple of God with idols? for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people.
Wherefore come out from among them, and be ye separate, saith the Lord, and touch not the unclean thing; and I will receive you.
The passage in II Corinthians couldn’t be more clear (and can be applied to more than just a marriage relationship), but no mention is made of difference in skin colour as being a bar to marriage between Christians. To use Deuteronomy 7:1-4 to forbid interracial marriages among Christians is faulty application based on faulty exegesis.
The fact that Bob Jones University did change its dating policy showed that either BJU had been lying for years--i.e., their position hadn’t really been based on the Bible--or that as of March 3, 2000, the university was no longer basing its position on the Bible. Either way, BJU’s actions weakened its claim to be a fundamentalist Christian university.