First, the Bible teaches that the human race was created by God from one original man (Genesis 1-2), whom God named Adam. In truth, there are not many races, but only one race -- the human race. Darwinism promotes racism, creationism should promote respect for every human being.
All mankind is lost in sin. All have sinned and fallen short of the glory of God. Jesus said no one is good except God (Mark 10:18). Our different cultures, nations, and ethnicities love to compare and contrast ourselves to each other, when we ought to compare ourselves to Almighty God. When we do that, we should be humbled and see we have no basis for pride.
All peoples are welcome to God through Jesus Christ. In Revelation 7:9, John sees representatives from every nation, tribe, people, and language around the throne of the Lord. In heaven they retain their all human attributes, yet they are united in the worship of God. So should it be here.
There are ridiculous theories that have been taught to justify white superiority or some other race's inferiority, such as the so-called curse of Ham, or the idea that demons interbred with humans and produced the Nephilim. But the curse of Ham was really on Canaan (his father Ham representing him as overseer of the family), and was fulfilled by the Canaanites when Joshua destroyed them in the Promised Land. And even a child can read Genesis 6:4 and see that the Nephilim (which means "giants") were not the product of the sons of God and the daughters of men. Perhaps Goliath was one of the Nephilim, long years later.
God is also clear that He hates the uneven scale (Proverbs 11:1). Favoritism in the law-courts or the marketplace come under God's curse. God is a God of justice, and he demands of us the same fairness and impartiality He upholds.
Becoming born-again just by itself doesn't instantly cure attitudes of unfair favoritism, or hatred. But it makes a real start possible, because of the presence of the Holy Spirit in the person's heart. Christians need to be taught the Bible on this subject as part of their growth in faith, just as they need to know how it applies in other ways.