There are some who insist that the Bible condemns race mixing. Oddly, there are others who insist that the Bible has nothing to say about it, at least in the New Testament, and anything the Old Testament has to say is specific to the ancient Israelites and has no significance to us today except perhaps as a warning not to marry outside the faith.
I think the true answer is a bit more sophisticated than either of those perspectives.
There has been much confusion in the United States regarding this issue since the two primary nations of the US, the English American Nation and the African American nation, are imprecisely referred to as two different “races”, the Whites and the Blacks. Thinking of them as “nations” (or “tribes”) should help clear up some of the confusion.
With the resurgence of nationalism there is bound to be some befuddlement regarding this issue, so I will do my best to follow a train of logic from the available information to figure out what the Bible has to say or imply about mixed marriage (if anything).
First of all, the plain fact is that when different tribes live close to each other, there’s always going to be some intermarriage. If Medieval Jews could not prevent their daughters from falling for Christian lovers, no other ethnic barrier stands a chance.
The Old Testament contains multiple injunctions warning the ancient Israelites against marrying outsiders, but for some reason there are also multiple stories about Israelites who married foreigners and were not condemned for it. This is not a contradiction. There was no condemnation if the foreign women were converts. In other words, there was no problem if the wife adopted her husband’s religion, worldview, and culture. Their children were not seen as “mixed” but as full members of the father’s tribe.
King David, for example, was of mixed ancestry, but he was never denigrated as any kind of mulatto or half-breed.
There is another side to the coin, however. The half-tribes of Manasseh and Ephraim, two of the most rebellious tribes of Israel, were the result of their progenitor Joseph marrying a foreigner, and their rebellious behaviour is often traced back to the influence of their mother, even though we may assume she converted. Joseph was a righteous man and was not condemned for marrying a foreigner, but his marriage did lead to complications.
So if a Biblically-derived argument can be made about mixed marriage, it is the same that common sense would indicate: that sometimes mixed marriage is OK, but it can lead to very unpleasant complications, especially for the children.
Any argument against mixed marriage has to be derived from specific circumstances, such as whether the children are likely to be victims of ostracism or whether intermarriage is being used as a method of conquest---such as when Egypt attempted to subsume Israel by forcing all their young women to find Egyptian husbands (Exodus 1).