For the record, the Liberal Left mostly cannot support Critical Theory in any of its guises, including Critical Race Theory (even if it doesn't mind accepting--Liberal, after all!--that some valid insights have come from such endeavors), since, as you point out, Critical Theory was founded as an attack on liberal values in favor of a different way to organize society.

A fair number of people on the Left take liberal values very seriously, "centering" not group identity but individual flourishing, rational argumentation, freedom of expression and to the extent possible action, and so on. The primary quarrel that the Liberal Left has with Conservatives in this regard is that Conservatives are, well, conservative, and fail to adhere to these values when they run up against a tradition to the contrary. (A secondary quarrel is over how best to accomplish these things--whether nurture or challenge better enables flourishing, for instance.) Nonetheless, the flavor of Critical Race Theory that you describe is not compatible with the values of the Liberal Left, and those people in the Liberal Left who are exposed to such ideas tend to reject the method.

So I don't think your repeated references to the "liberals" is really correct. I think you mean "Progressives" (or whatever is further in that direction). "Left", as a synonym for "whoever gets to yell the loudest on that side without getting completley shouted down" is fine, I guess.