There are many circumstances which bring extra difficulties to a marriage – difference of race or culture, difference of education or ability, marked difference in social background, wide disparity in age, etc. It is really the choice of the couple themselves.
There is only one marriage relationship which is forbidden by God. God's people are forbidden to marry those who do not believe.
We can see the wisdom in this. God intends marriage to be a permanent relationship for the ultimate, mutual benefit of both. Anyone who believes in God and truly wants to serve Him, cannot find real fulfillment and happiness with one who does not. Their spiritual growth will be greatly hampered.
2 Corinthians 6 says:
"Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness?"
Marriage is surely the closest "yoking together" possible.
1 Corinthians 7:39 is very much on the subject.
"A woman is bound to her husband as long as he lives. But if her husband dies, she is free to marry anyone she wishes, but he must belong to the Lord."
Corinth was a very cosmopolitan city. The church there was made up of Jews and Gentiles of many different races. So, it is very significant that it was to the church at Corinth, that this instruction was given! Race is not mentioned.
In Old Testament times, the people of Israel were forbidden to marry those of the surrounding nations. Deuteronomy 7 says 3.
"Do not intermarry with them. Do not give your daughters to their sons or take their daughters for your sons, 4. for they will turn your sons away from following me to serve other gods, and the Lord's anger will burn against you and will quickly destroy you."
Notice carefully the reason given. It was not a matter of genetics or culture, but of religion. The people of the surrounding nations were idolaters. Where individuals did come to believe they were fully accepted and married Israelites. For example Rahab, a Canaanite, and Ruth a Moabite, appear in the ancestry of Jesus himself. Matthew 1 verse 5.
So we have a consistent picture. In Old Testament times God was working with one nation - the Jews, and so His people were forbidden to marry those who did not believe in the living God. Today the Gospel goes to all nations and the only restriction on choice of marriage partner is "only in the Lord".