I don't think the way I said it was ambiguous at all, but I will expand.

I do think the term has other meanings, such as the natural one that results from the common adjective + noun construction used to mean "not really the thing described by the noun, but something roughly analogous mediated by the adjective". (Some critics might snark that the adjective "social" is commonly used in this way.) In this case, something that is not Marxism, but which treats culture analogously to how Marxism treats class and economics. Which is to say: identifying oppressor and oppressed groups, asserting a need for revolution, having a particular notion of what equality (or "equity") looks like, adopting a strongly collectivist/anti-individualist attitude, etc.

It also could refer to the specific work of the Frankfurt school, with or without the belief that those ideas are inherently "subversive", with or without the allegation of "intentional academic effort" to spread those ideas.

(And it certainly doesn't depend on caring about the religion or ethnicity of the original academics. Just like any generic reference to "elites" isn't inherently anti-Semitic.)