African American

is technically correct. The problem is how that theory is applied. The fact is, the concept of "Whiteness" and "Blackness" are basically the analogue to bourgeoisie and proletariat in Europe; not that the latter doesn't exist here, but essentially we have two (and really three if you take cismale versus not-cismale into account) dynamics of base versus superstructure intersecting in America, and they affect the entire nature of classism.

read below if you want to hear a bit of heavy Marxist class/race analysis :

Essentially the key to the American class structure is the concept of "Whiteness", aka, the group of people that are considered full people in society. The thing to understand here is that it's a very sliding scale - at some point, European groups like Spaniards/European Hispanics, Chinese, Slavs, Irish (!), Italians (!!), and even Germans (!!!) were not considered "white" (which is why some of those groups were enslaved, and others used as cheap labor that wasn't quite as bad as slavery but wasn't too far off). Thus we see that "whiteness" has no relation to European descent, so much as it relates to where you are in the power structure and how much and what kind of resources one has access to.. Whiteness has adapted however, by incorporating these groups, giving them more privilege, and thus maintaining the underclass (Irish, Italians, Slavs, and even some Hispanics became "white", Asians are still affected by racism but they've been encouraged as a model minority and as such have gotten more access to resources)

Right now it's even trying to adapt by elevating people of the most marginalized groups as long as they adhere to the power structure (Ben Carson, Milo Yiannopoulos , Caitlyn Jenner as examples.). While one may struggle with class oppression as a "White" person, there is a powerful psychological wage associated with being "White" that mitigates that oppression, as well as provides avenues for escaping it (basically the proverbial American Dream, and a huge source of the myth that if you work hard enough you'll make it). For example, even poor whites get better access to services, infrastructure and opportunities than non whites.

(I'd argue that some groups of nominally "White" people are in the process of being kicked out of the club that that's outside the scope of this conversation)

So the struggle regarding "White" people in America is to get them to voluntarily *give up* their Whiteness, to give up the preferential access to resources, prestige and respect that Whiteness confers, so as to struggle with marginalized groups for a better, more equal world that in the long run, will serve them better. Of course, this is hard and risky so people would rather not deal, and would pretend that it's not THAT big a problem, even if you're nominally left. Trying to argue that "fixing class will solve everything" doesn't work, not because class isn't important (it does intersect with everything) but because it betrays a lack of understanding of how class in America works.