I think this is largely true but not complete: the interaction between race and class in the US is complicated. Race is frequently used to divide people who on the face of it should be united by class issues.

There’s a famous LBJ quote about this:

“If you can convince the lowest white man he's better than the best colored man, he won't notice you're picking his pocket. Hell, give him somebody to look down on, and he'll empty his pockets for you.“