I completely agree they reinforce each other, but what your attempt at race reductionism that turns into outright gaslighting hides is a fact universalists have known for decades:

“If a white man wants to lynch me, that's his problem. If he's got the power to lynch me, that's my problem. Racism is not a question of attitude; it's a question of power. Racism gets its power from capitalism. Thus, if you're anti-racist, whether you know it or not, you must be anti-capitalist. The power for racism, the power for sexism, comes from capitalism, not an attitude.” —Stokely Carmichael