Whites aren't just skin color.

Who said it was?

They will actively select for white skin but not for the rest of the white genes

That's not how genetics work. I don't even know why you'd think this when you can obviously see some mulattos with white phenotypic traits other than white skin, and the average IQ being much higher than African-Americans and being very close to whites.

https://en.wikipedia.org/wiki/Eyferth_study

When we examine the genes passed down we can objectively see many genes are carried on from the white parent that influence behavior and the brain too.