It's not a reasonable and realistic premise - it's word salad trying to scare.
Thank you for that, sir :) True and funny at the same time.
Postmodernism rejects any theories of the world that have any kind of absolute structure, while marxism is explicitly about defining such absolutes. In marxism, all people are either workers or capitalists (or outside the system); any good has an intrinsic value, and any work has an intrinsic plus-value; and on and on.
You can also see this in the art favored by countries which liked to claim to be marxist-leninist (though they weren't). Far from being post-modern, it was in fact traditionalist and realist.
[1] https://www.newyorker.com/news/dispatch/was-the-philosopher-...
I do admit that I may be completely off base, I know very little of her beyond what I could find on Wikipedia (which does list her as Marxist, but provides no further insight on why) and a handful of scholarly articles.
Note: a much better example you could have given was Slavoj Žižek, to which I have no answer..
On the other hand, Chomsky supported many socialist and even marxist leaders. Like Chavez nationalizing every profitable sector of the economy. Note this is very not anarchist as it concentrates power in the state and a rulin elite. Perhaps he was blinded by his anti-war and anti Western establishment feelings. Who knows.