If you click on the hyperlink Paul Graham hyperlinks as "academic bogus," you'll find a google scholar search for "hermeneutic dialectic hegemonic whiteness." First of all, I don't think Paul Graham read those 5000 article returned by the search. Instead I think he just typed in a chain of academic words he thought represented useless academic research, and then told himself these "tee-hee postmodern bogus." I think…
I'm upvoting you because I think you make a fair and well-thought-out argument. With that said, there's certainly a hand-waviness to "soft" fields like gender studies or ethnomusicology (I took classes in both, just out of curiosity). And no matter how much you think Derrida or Focault contributed to philosophy, I would argue it pales in comparison to their Analytic contemporaries (Godel, Lewis, Anscombe, Moore, etc.…
I don't know anything about gender studies, but regarding ethnomusicology, you can be assured that it is a bona-fide, hard subject, even involving and motivating non-elementary math. The study of timbre and harmony in western music is rather dry, since it is overwhelmingly dominated by wind and string instruments that have one-dimensional, harmonic spectra. Even western percussion instruments are painstakingly tuned to have integer partials. The study of ethnomusicology opens an incredibly wide field of different types of instruments and their harmonies that is a godsend for modern musical theory (and, in turn, it helps to understand western harmony as a concrete particular case among an infinite ensemble of possibilities). See, e.g.
https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...
this is a serious textbook about ethnomusicology and linear PDE on Riemannian manifolds.
What were your ethnomusicology classes about? They might be really bad, if you ended up thinking that it is a "soft" subject.