> This might be contrasted with “postmodern Marxism” or “postmodern neo-Marxism” which is some kind of pseudointellectual epithet but is seems fundamentally incoherent. Postmodernism rejects grand narratives about society, but Marxism itself is a grand narrative (namely, that capitalist society should be framed as a class struggle between workers and capitalists).
Postmodern Marxism is a real thing too. See for example yet another Duke University Press book (Duke University is really into this kind of stuff for some reason) from 2001, "Re/presenting Class: Essays in Postmodern Marxism" [0]. Another more recent book is "The Condition of Digitality: A Post-Modern Marxism for the Practice of Digital Life" (University of Westminster Press, 2020) [1]
Are postmodernism and Marxism inherently contradictory? Well, "postmodernism" is a very broad and amorphous school of thought. The idea of postmodernism as opposition to "grand narratives" is due to Lyotard, and yes that idea seems rather incompatible with Marxism, at least in its classic form; but other postmodernist thinkers emphasised different ideas, whose incompatibility with Marxism is less obvious.
I also am picking up on the fact that you are obliquely referring to Jordan Peterson, who is known to use the phrases “postmodern Marxism” and “postmodern neo-Marxism”. Honestly, I've never paid him a great deal of attention – I'm neither one of his fans nor one of his haters, I'm just not that interested in him. So, I can't say whether he is using the phrase "postmodern Marxism" in the same sense as those academic books I cite do, or in a different sense.
> The cultural Marxism discussed in 60s and 70s academia is not the same thing as what the Norway terrorist was referring to in his manifesto.
I don’t know about that. Let me put it this way: the World Zionist Congress (WZC) is a real thing, an international conference that was first held in Switzerland in 1897, and it was held for the 38th time in Jerusalem in 2020. So the conference is not a conspiracy theory. But, if you go looking for them, you will find antisemites who will tell you that the WZC secretly controls the world’s banks and governments-that is a baseless conspiracy theory. However, even though we have both a real world factual discourse about the WZC and an unhinged antisemitic conspiracy theory about it, that doesn’t mean that the two discourses are using the term “World Zionist Congress” to mean fundamentally different things-no, they are both talking about the same thing. In the same way, just because Breivik talked about “Cultural Marxism”, doesn’t in itself prove he was talking about something different - he could be talking about the same thing, but making baseless/unhinged claims about it, and wrongly using those claims to justify his senseless mass murder of innocents
[0] https://books.google.com/books?id=0PdqvSOo-rgC
[1] https://books.google.com/books?id=qSkNEAAAQBAJ