So many explicitly racist movements have also been explicitly [anti-]capitalist
Name some, including the substance of them being anti-capitalist. The KKK aren't anti-capitalist. The Nazis aren't anti-capitalist. The Confederates weren't anti-capitalist. Mind you, all of these groups and other racist movements oppose some version of "globalization," something the developed capitalist forces push, but they are not thereby rejecting all of capitalism, because the system that they call for is still capitalist, just degenerated to earlier forms, the national or local depending on which movement it is.
Racism is a tool of tribalism and collectivism. Capitalism is an individualistic system.
I think individualist/collectivist is a much less helpful way of analyzing ideologies than a lot of liberals think it is, but that's partly because it question-begs the supremacy of liberal ideology, which means I don't think we'll come to an agreement.
Anyway, pretending they were useful terms, I still think this is a bad argument. When you live within a capitalist society and aren't looking to overthrow it, it is a coherent idea to create collectives within a system that is philosophically oriented around the individual power of property-owners, that's what labor unions are. Most fascist movements are theoretically a racial version of this, white people (or whoever) collaborating to fuck over minorities to save themselves that much competition. That's what Krystalnacht was, for instance, a white-German community effort to drive out the competition represented to them by Jews.
The unavoidable fact of capitalism is that it relies on pushing most of society into the same general social class (workers, as contrasted with owners; employees vs employers) and likewise makes production a massive group effort, though that group effort is dictated by an individual or an oligarchy who own the instruments used in that production. You can try to appeal to these workers who make up most of society on an atomized, liberal basis, sure, but it's no less coherent to draw lines of common interest between them, most often something like race or religion that is convenient to capitalists, because the capitalists can say "look, I'm white (or whatever) too, I'm on your side!" even if they truly aren't because they are only seeking their own profits.
This is about a third of an explanation of the material basis for fascism. Probably the most critical element is that capitalist expansion hits some limitation, be it international competition or just all of the market already being claimed. The reason, the real motivation, for the racial terrorism I described above despite merely deflecting worker ire, is that by "clear cutting" more space open for your market share by slaughtering competitors, people sitting on land you want, etc., you can gain more room to grow, although this too only lets you grow temporarily until you bump into your new limits, so you need to keep killing inconvenient people to keep growing, and that's more or less how the Nazis worked, both internally by picking out minority after minority, and externally with their continuous invasions and "lebensraum" and so on.