As much as Chomsky may have been incorrect, I think it is foolish to call him "depressingly ignorant" without justifying your statement. His international recognition both in his field and in his commentaries did not appear out of nowhere.

I think I could justify it... but it'll take some work, and is unlikely to ignite any sort of productive discussion - so I'll just edit that out.

This seems to be the theory of multiple intelligences + g-factor denialism + credentialism taken to an absurd extreme. I see this idea used so often in arguments, I think it ought to be a formal fallacy. I'll call it Silo Fallacy for now. The idea that Einstein was as capable of making an argument outside his lane as the person on the street is ridiculous enough, but Chomsky identifies as a "public intellectual" - that is his lane.

I'm not very proficient with the "theories" you've mentioned. I'm more into facts. The quote is not offensive and is not about Chomsky. Personally, I find it empirically true. YMMV

How to define a nonscientific problem. There is none. All sociology problems are related to psychology that is related to biology which is related to chemistry which is related to physics which is related to math. https://xkcd.com/435/