The legitimacy of these critical theories seems to rest on Kripke's invention of so-called "modal logics," which I understand were initially presented as a progressive reaction in philosophy departments to the positive logics derived from maths. The criteria for logic is that it "adds up," or more accurately, our rules about logic and consistency (from Gödel, Russell, and others) were only deemed to represent reality if the logical system could represent arithmetic. Kripke seemed to propose that if you revisit and start with logics that cannot represent arithmetic, you still get consistent logical forms, which are sufficient for expressing a much larger range of phenomena. Because sure, if you produce nonsense, nonsense can represent anything. It's the definition of magical thinking, but within a couple of decades, it was being presented as the "formal" logical underpinnings for a variety of essentially marxist ideologies of different intersectional flavours, where they produce the same circular bullshit with only a few words changed, and with the same object in mind: dissolution of meaning and the destruction (neutralization) of discourse as a means to create chaos and to seize power.
It is a rhetorical system for protagonizing antagonists. We can sythesize these ideologies pretty trivially and inject them into naive minds that turn them into either activists, or neutralize any resistance to them because they're just baffling gibberish with the threat of political consequences. Nobody wants to admit they have been fooled or taken, and its easier to attack the people who point it out than to admit that you have been bullied and hustled by highly trained pros.
High school teachers judging middle school debate clubs aren't equipped to handle this, but theory is teaching kids to rhyme out ideologies that are entertaining, and even charismatic, but they're nothing but the same old tropes of the 20th century and its grisly consequences.