True, but a race war is us against us, a class war is 90% vs 10%... the 10% currently in power.
The southern strategy was to literally go against anything that would benefit black people, EVEN if it benefited poor white people too, because it's better to be miserable and white than to let a black person get ahead of you from government handouts. This was the entire strategy of the GOP(still is) since the 1950s.
I think the centrists (which may even just be a 'role' they play) goal is to keep both parties fighting on fringe issues like abortion and guns so we don't stop to reevaluate how much we're being fleeced by the govt to create $$ for their buddies in the oil and defense industries. Their purpose is to appear w/ the others, but only slightly and to ensure that the status quo remains intact.
Lee atwater said in 1981:
“As to the whole Southern strategy that Harry S. Dent, Sr. and others put together in 1968, opposition to the Voting Rights Act would have been a central part of keeping the South. Y’all don’t quote me on this. You start out in 1954 by saying, ‘N*er, n*er, n*er’. By 1968 you can’t say ‘n*er’—that hurts you. Backfires. So you say stuff like forced busing, states’ rights and all that stuff. You’re getting so abstract now [that] you’re talking about cutting taxes, and all these things you’re talking about are totally economic things and a byproduct of them is [that] blacks get hurt worse than whites. And subconsciously maybe that is part of it. I’m not saying that. But I’m saying that if it is getting that abstract, and that coded, that we are doing away with the racial problem one way or the other. You follow me—because obviously sitting around saying, ‘We want to cut this’, is much more abstract than even the busing thing, and a hell of a lot more abstract than ‘N*r, n*r.’ So, any way you look at it, race is coming on the back-burner.”
When I read this a few years back, it totally just clicked - that this is the entire economic platform of the right. Working class republicans support things that go against their own best interest (medicare for all for example), simply because they damn well don't want non-whites to have nice things, even if it means they don't get to either. Asinine as hell, but generations of racism and bigotry don't generally create tolerant people wanting to switch things up.