For instance, AAVE is seen as "low class" despite there being plenty of speakers of it who are not lower class at all.

The kind of racial reductionism we've seen come from (often well-to-do) liberal circles that presents being white (or not Black) no matter the class background as a walk in the park is a dead end of course, but we have to be careful to recognize that there are a number of structural racial problems that don't always have a targeted class character (unless you get to the very upper echelons of wealth).

That said, the popular discourse in America is woefully under-prepared to understand class divisions between and within racial groups. That lack of nuanced discussion is why we end up favoring an understanding that is fully rooted in upper-middle-class experiences and study.

A Black writer who grew up poor, went to a city college and still lives in their neighborhood will never get an op-ed position at the New York Times no matter how good of a writer they are, so their experience gets completely lost in the mainstream, despite being so important to understanding class and race in America.