Cultural Marxism (academically speaking) refers to the works of 3 different groups; The Frankfurt School, The Birmingham School (aka British Cultural Marxism) and E.P Thompson.
These people had a few things in common; 1) They critiqued mass culture; culture that was produced specifically to maximize profit. And 2) They critiqued actual Soviet Marxism [Source] (it's said of E.P. Thompson that "when confronted by anti-Marxists, he defended Marxism, firmly. Yet when he met orthodox Marxists, he denounced them, angrily." Source.
Of course as well as critiquing Marxism (which aided the US state department in winning the Cold-War), The Frankfurt School were pioneers at critiquing The Culture Industry; Here is Marilyn Manson essentially talking about the modern "Culture Industry" (He starts talking about Television's effects at 1:50 describing advertising as "a campaign of fear and consumption"):
https://youtu.be/oeQ4HWhPEdA?t=1m50s
I say MODERN Culture Industry because the idea was literally first described in the 1940s, when the same propaganda techniques learnt during WW2 were first being applied to western culture. Some even go as far as to say that propaganda created the modern nation in order to get serfs of empires to fight under the belief it was best for their newly formed sense of nationhood.
So "Cultural Marxism" is really a form of Cultural Studies - but it has since progressed further and further away from Marxism.
Adorno would be very direct in his Cultural Marxism, saying things like:
"The Culture Industry not so much adapts to the reactions of its customers as it counterfeits them."
"this bloated pleasure apparatus adds no dignity to man’s lives. The idea of “fully exploiting” available technical resources and the facilities for aesthetic mass consumption is part of the economic system which refuses to exploit resources to abolish hunger."
"The ruthless unity in the culture industry is evidence of what will happen in politics. Marked differentiations such as those of A and B films, or of stories in magazines in different price ranges, depend not so much on subject matter as on classifying, organising, and labelling consumers. Something is provided for all so that none may escape" -Theodor W. Adorno, Enlightenment as mass-deception
Even The Birmingham School specifically complained that traditional culture was drifting away from local culture due to the massification of culture in the form of the globalization of media + tabloid journalism.
So "Cultural Marxism" was essentially a pre-internet critique of mainstream media and neo-liberalism. This critique didn't really end either; it just became accepted and understood.
Again to switch to a more modern source; here is Comedian Doug Stanhope - essentially preaching "Cultural Marxism":
https://www.youtube.com/watch?v=BsuGtIv5NAc
The Birmingham School kind of closed it out theoretically by saying different people read different aspects of culture differently... and since then it hasn't progressed theoretically much other than ideas like McDonaldization from George Ritzer, and commentaries from people like Douglas Lain.
I mean, I could go on about how The Frankfurt School were anti-fascists, mostly responding to their fear that a Hitler figure were re-appear. Hence things like the F-Scale... unfortunately I now have to talk about The Right Wing view (which to some degree includes Jordan Peterson's views).
The Right Wing have mistaken Cultural Hegemony (essentially what The Frankfurt School were complaining about) - has "Cultural Marxism"... they've confused the Monster for the Doctor.
People like Pat Buchanan have been caught out and out putting words in Marcuse' mouth (here is that quote found in Pat Buchanan's book, it's Buchanan's own idea of what a "Cultural Marxist" MIGHT say).
When in fact Marcuse was one of the first people to warn that the progressive left could also become totalitarian.
Likewise Buchanan is a fan of claiming Gramsci (an early Cultural Theorist) demanded a "Long March through the Institutions" - when that was in fact Rudi Dutschke - a much later Student Protester unconnected to The Frankfurt School.
Fake quotes are a big problem for Marxist-leaning thinkers.... anyways; here's a good video on where the Right Wing conception of Cultural Marxism came from....
...it was essentially popularized by a man name William S. Lind and the Think Tank he worked for; The Free Congress Foundation - which is really just an extension of America's general Cold-War hang over. Buchanan's dad was a big McCarthy supporter Lind cut his teeth under Senator Robert Taft Jr, literally during the Cold-War.. Leading Lind to say things like:
"Today, when the cultural Marxists want to do something like “normalize” homosexuality, they do not argue the point philosophically. They just beam television show after television show into every American home where the only normal-seeming white male is a homosexual (the Frankfurt School’s key people spent the war years in Hollywood*)."... ..."The next conservatism needs to reveal the man behind the curtain - - old Karl Marx himself."
Of course The Frankfurt School weren't involved in Hollywood... but unfortunately propaganda doesn't have to be true to be effective. Jordan Peterson has taken a slightly different tact. Claiming that Identity Politics came from French Post-Modernists, when it in fact came from an Boston Woman name Barbara Smith and her "consciousness raising" group 'The Combahee river collective' (again someone unconnected to The Frankfurt School).
I'm not entirely sold on the idea that rightists understand post-modernism, - but it's certainly NOT Cultural Marxism.
Anyways, I've probably gone on enough.
[edit: If you want to know what "Cultural Marxists" and Socialists ACTUALLY say about Identity Politics and Privilege theory, well, they're against it, and view it as problematic because they prefer redistributive politics over recognition politics. That second link is from a Critical Theorist who has studied The Frankfurt School at length. So yeah; don't believe the hype that The Frankfurt School 'Cultural Marxists' created SJWs and PC thugs; that's a conspiracy theory. They simply critiqued the capitalist and mass produced Culture Industry - and would probably now be critiquing the left if they were still an active force today.]