Cultural Marxism is an extension of the older idea of Cultural Bolshevism, which was a term used by Nazis (as in, the original 1930s-1940s ones) as an attack on modernist art and philosophy by associating them with the Bolshevik Revolution, and claiming that the Bolsheviks were using modernist thought as an attempt to subvert traditional values. It was antisemitic because it also involved the conspiracy theory that the Bolshevik Revolution was actually a Jewish plot and that the Soviet Union was controlled by Jews.
Essentially, modern art, philosophy, and media was Bolshevik, and Bolshevism was Jewish, and the Jews were a priori bad, therefore modernism (and thus many critics of the Nazi regime) were bad and couldn't be trusted. (And moreover, the Jews controlled the Bolsheviks, and the Bolsheviks controlled modernist thought via cultural Bolshevism, therefore modernism is just a Jewish plot.)
The modern variant is Cultural Marxism, which essentially makes similar claims about post-modernism. In fairness, Cultural Marxism tends not to be so blatantly antisemitic, although many of its early proponents in the 90s and 00s were themselves antisemitic. That said, it retains the same basic structure of claiming a conspiracy by a small group of philosophers (typically the "Frankfurt School") to subvert traditional values with a corrupt philosophy.
It is principally antisemitic in that it is simply a rehashing of an older antisemitic conspiracy theory, proposed predominantly by antisemites. The parts involving Jews have been filed off to make it more palatable to a mainstream audience, but this is a pretty thin veneer over what is fundamentally a Nazi-era conspiracy theory.
It's worth reading the Wikipedia article on Cultural Bolshevism (https://en.m.wikipedia.org/wiki/Cultural_Bolshevism) and following some of the links from there to understand the progression between the two ideas, and why people are understandably quite concerned about how mainstream the idea of Cultural Marxism has become.
I was ignorant of nearly all the terms you used, so bear with me, but seems like you're saying it's antisemitic because it seems to be an extension of a previously idea which was used as part of an antisemitic campaign.
You say "The parts involving Jews have been filed off ...". To be me, this doesn't necessarily suggest it's "to make it more palatable to a mainstream audience".
The whole thing seems heavily loaded to me (someone who is coming to these terms fresh-ish). I've heard some murmurings around how modernism is a "lefty" idea, and how criticism of modernism is a "right wing" idea, and that's falling into place a bit more now.
I think it's a bit simplistic to say that modernism is "lefty", especially today, when it's probably more of a conservative principle. (Postmodernism tends to be more accepted by the left, which might be what you were thinking of, but even that isn't always a very useful generalisation. The whole concept of being "post truth", which was Trump's whole playbook, is a very postmodern idea.)
I think the key thing is that the modernism/postmodernism/left/right thing doesn't really matter here, because both Cultural Bolshevism and Cultural Marxism are both fundamentally conspiracy theories. They both claim that modernism (and postmodernism respectively) are attacks on our society by a small group of bad actors who have infiltrated society in some way. (And to be clear, there is no evidence for these claims at all.) In Cultural Bolshevism, those bad actors were explicitly linked to the Jews. In Cultural Marxism, that explicit link isn't often there, but given the connections to the previous antisemitic theory, and the fact that many of the early proponents were explicitly antisemitic, it's difficult to separate the two entirely.
> While the term "cultural Marxism" has been used in a general sense, to discuss the application of Marxist ideas in the cultural field, the variant term "Cultural Marxism" generally refers to an antisemitic conspiracy theory.
I spent longer than I care to admit diffing "cultural Marxism" and "Cultural Marxism". I think this is the problem though; they're two different things, that happen to be written the same.
You cannot really make a connection to antisemitism by certain key words. While cultural Marxism certainly has some baggage, but it does not infer any hostility to Jews. It can do so, but it shouldn't be regarded as doing so.
It’s the only usage of “cultural Marxism” that’s ever been used, and any conceivable cover that might be plausibly deniable is blown by contrasting it with Marx.