I grew up in Georgia and encountered many Christians that still thought interracial marriage was unGodly. So I asked them. Here were some of their responses:
1. God split the races at the Tower of Bable. To unite them in marriage is to go against his will.
2. God specifically says not to marry others of another race. Yeah, Moses did and he was wrong, but God decided to overlook it. (The Israelites knew it was wrong and pointed it out to God.)
3. Noah cursed the black race. We don't need to bring his curse over to caucasians.
4. God did not make the races equal or else he never would have favored one over the others. Therefore, it is God's will for the races to remabe in balance and unequal.
You can find some of these quotes in court cases like "Loving v. Virginia" where the judge said:
Almighty God created the races white, black, yellow, malay and red, and he placed them on separate continents. And but for the interference with his arrangement there would be no cause for such marriages. The fact that he separated the races show that he did not intend for the races to mix.
In 1948, about 90% of American adults opposed interracial marriage. In 1967, about 72% opposed it. It broke even around 1991 and has kept declining. So just looking at 1948 where about 90% of America is Christian, you have most of them against interracial marriage. And I bet they all said that God was on their side.
You will see the exact same thing happen with homosexual marriage.