That’s a common misconception because various intellectual movements have called themselves “critical theory.” The problem is the words “critical” and “theory” are both so generic and flexible they can mean many things, even in combination.

CRT is founded in the “critical theory” within the study of law. https://en.wikipedia.org/wiki/Critical_legal_studies. Some with Marxist leanings became involved in it, but critical legal theory was never about Marxism or being antithetical to Western culture. Of course, the right-wing slaps those labels on everything that questions the prevailing hierarchy,

You may be thinking of the “critical theory” of the “Frankfurt School,” in particular Max Horkheimer and Theodor Adorno in the 1930s. They were unabashed Marxists, and there are some people today who would say they are “critical theorists” who also call themselves “Marxists,” but they are a minority. The two main critical theory philosophers of the past 30 years, Jürgen Habermas and Axel Honneth aren’t Marxists. I earned my PhD at a philosophy department specializing in “critical theory” and no one there were Marxists, and I’m a critical theorist, and I’m no Marxist. No one I’ve ever met or read within Critical Theory in the past 50+ years has been urging a “Marxist revolution.” Believe me, they are all quite bourgeois.

You ask a great question on the difference between philosophy of race and the critical philosophy of race, a question I deal with at this point in my online lecture: https://youtu.be/IUV2WItyUOI?t=244.