One can always find exceptions to the rule.
But studies have also shown that income mobility regardless of race is statistically rare.
I've heard a lot of classist comments from both White people (calling people "red necks" and "trailer trash") and upper income black people ("I don't want to live in a majority Black neighborhood around "them people")
But if you're of the wrong race, that clearly can't be your fault, and you can't "fix" it.
That split in how we think about class and race may be the underlying mechanism as to why we can't talk about both class and race at the same time.