Interesting discusssion, thanks. I think we are fundamentally debating classic Marxism as an economic theory against various strains of neo-Marxism here. Such as Antonio Gramsci, for one:

... renovate the existing intellectual activity of the masses and make it natively critical of the status quo. His ideas about an education system for this purpose correspond with the notion of critical pedagogy ...

"Cultural marxism" is not my term though. As a criticism of "cultural hegemony" it might be Gramsci's own invention, but as I said I don't really care what it's called... There is also "Marxist cultural analysis":

Since the 1930s, the tradition of Marxist cultural analysis has occasionally also been referred to as "cultural Marxism", in reference to Marxist ideas about culture

Wikipedia also has an article called "Cultural Marxism conspiracy theory" which is what you're probably referring to. I'm not. We shouldn't go on pretending that these ideas don't exist or are willful misrepresentations though. And if we do need to adopt a derisive term for this kind of ideological attack by borrowing it from Gramsci's critics, then so be it. Heck, even "capitalism" comes from Das Kapital and we use it to this day.

To be clear though, I really don't subscribe to any "Jewish question" baggage that comes along with these terms. We need a common language though, and I guess I would call the kind of ideological revolution called for in the quote above (through arbitrary definitions of oppressor/oppressed categories) to be some kind of cultural marxism. That's my colloquial definition at least, and it comes from reading Gramsci, a bonafide (neo-) Marxist—not his persecutors.

Maybe you're right and it is actually possible to tease apart these ideas from postmodernism and nazism. But there are still core elements of (neo-) Marxism in there, and those distinct ideas are from a century ago have semantically drifted into each other into the mess we're seeing today. It's probably not helpful to quibble about old terms and instead talk about what's actually happening.

If I am an "ist" of anything I would want to call myself a pragmatist. I don't believe in the supremacy of the Right over the Left or vice-versa. They are both necessary to keep balance on different issues. Some things are necessarily better when socialized; many other things not. You said:

A core, fundamental portion of Marxist thought is of a continuous line of economic development

I fundamentally don't believe there is a continuous line. We need the ability to adapt and diversify our resources, and a singular theory or way of thinking cannot be helpful to all situations or avoid creating harm that it didn't account for.