The term is really just a shorthand reference to the kind of social, political, and ideological ideas that a "progressive" university student absorbs (or is expected to absorb) during the course of his or her 4+ years in a contemporary American university.
I explicitly asked for sources that are not on the far-right. The thing about the far-right versus academia is that I've got a fairly decent prior on the far-right rationalizing its ideological views, and a fairly decent prior on academia publishing things based on epistemic rigor rather than ideology.
And no, the Frankfurt School are not "cultural Marxists". This is a term nobody has ever applied to himself.
You aren't going to find that term used by the people to whom it's typically applied. They will probably use a more specific term like "Critical Race Theory", or "radical feminism", or "social justice".
But there's a continuum of thought between these otherwise distinct concepts, which is where the "cultural Marxism" name comes in, as a unifying tag.
The term is really just a shorthand reference to the kind of social, political, and ideological ideas that a "progressive" university student absorbs (or is expected to absorb) during the course of his or her 4+ years in a contemporary American university.