I am not defining capitalism as just everything bad, and capitalism is not as recent as you think.

No that's pretty recent, racism is millennia old. Furthermore, yes mixed economies exist, actually now they're basically the only thing that exists.

American society developed the notion of race early in its formation to justify its new economic system of capitalism, which depended on the institution of forced labor, especially the enslavement of African peoples.

I disagree that it was capitalism that needed racism to be justified, since slavery is anti-capitalistic. But yes, fake "racial science" was used to justify slavery, that however was not the origin of racism. Roman and Greek and many other empires used ethnic/racial division to justify their oppression. Even the Mongols whose empire was "cool and accepting" by ancient empire standards still had strong sentiments of a Mongol race being different from others.