What does racism have to do with theology? Nothing...and everything.
Nothing because racism is based on a lie, and as it is based on a lie, it does not really exist apart from that lie.
And everything because this lie attacks our most fundamental knowledge of God as our Creator.
Here's the lie: There are different 'races' of human beings.
This is an out and out lie. Growing up in the south among fundamentalist Christians I have seen this lie projected onto the pages of Scripture, but I have never found it in the Scriptures. And that is really something because I was told for the first twenty years of my life that it was there.
(Some disclosure is in order. I am a caucasian, southern, redneck, hillbilly. It gets better. My wife is from Mexico. I still live in the south. So I am going to step back and try to look at this as objectively as I can.)
I was told for the first twenty years of my life that racism was a biblical concept. I married at the age of twenty-one. (For the record, I never heard anything like this from my own parents. I am thankful that God spared my family from this sin.)
The simple fact of the matter, as we get back on topic, is that the idea of racism is not found in Scripture. We find different families, ethnicities, nationalities, and different 'colors', but never any kind of reference to different 'races'. That is because there is only one race, the Human Race. Adam's Race. We are all part of Adam's Race.
Biblically speaking, we need to be constantly reminded that Genesis 1-3 really happened. Those chapters are not outlines of symbolic language that explain creation in a mystical fashion. Those chapters give us the details of creation and the current state of mankind.
As regarding mankind what do we find? We find that God created man out of the dust of the earth. He then breathed into man the breath of life. (Chapter 2:7) This is after God states His intent in the creation of man as in the image of God for the domination of earth. (Genesis 1:26-30)
First, we find that God created the first man Adam. Adam was the only one. There wasn't any more. No monkey men who would later marry into family of Adam. Just Adam. His creation is unique. There has never been another man made in same way that Adam was made. Adam's wife was made from the rib of Adam, and later, in Genesis 3:20 it is stated that she is the mother of all living. That's ALL mankind.
Second, we see that not only the creation of Adam was unique, but the creation of mankind was unique. We are made in the image of God. Granted, the image is broken, but it is still there. There is not a lesser image of God in different nationalities or colors. We all are made in the image of God, and we all have broken that image.
Where did Cain get his wife?
Who cares? We know that he married a wife, and if the above statements are all true, then he married another descendant of Adam and Eve.
What about the curse pronounced on the children of Noah's son, Ham?
That curse did not change the chemical make-up of Ham or his descendants in any way.
What about the tower of Babel?
Languages were confused, no races were created.
Why did God tell the Israelites not to intermarry with the Canaanites?
It is true that God told the children of Israel not to intermarry with certain nations that surrounded them. And yet God allowed Rahab and Ruth to marry Israelites. Esther was encouraged to marry a Persian. The weighty matter we are able to discern is not nationality but worship. This is further supported in the New Testament by a parallel command for Christians not to be unequally yoked together with unbelievers.
The New Testament writers also tell us that Christ's death broke down any wall between nationalities that may or may not have existed in previous generations. Jews and Gentiles are equal in Christ.
Conclusion: The idea of various races is not supported or taught by the pages of Scripture.