At the risk of falling for a joke, I'm not sure "critical thinking" means what you think it means. It just means thinking objectively about things before making judgments, it has nothing to do with criticizing people. The things one criticizes are our own beliefs and reasons for believing them.
What do I believe? Why do I believe that? Why do I feel that evidence supports that belief, but not this one? For example, I can explain in a fair bit of detail why I believe that the Apollo landing was not faked. I wouldn't normally bother to explain those reasons, but all of them are based on beliefs and evidence that I've read about, and most of those beliefs are subject to reversal should counter-evidence surface.
I think of critical thinking as the art of being critical toward oneself when one is thinking.
In other words, when I read something and hear myself think, "oh yeah, that sounds right", there is another part of my mind that thinks, "maybe not".
Critical thinking is precisely what could have spared us from all of that 'cultural marxism' you mentioned, or at least, to do it in a way that is... constructive.
"Critical theorists" are the people who fetishize "critical thinking" and all it got them was to embrace cultural Marxism.
Constructive thinking is far better than learning how to shit on people, as the skill of critique teaches us...