I agree with your statement except that part.
W.r.t coding, learning functional programing will help you in many ways. Learning category theory will just allow you to say "ah I've seen that concept before" - but it won't really help much.
“everything everyone else says is useless is useful”
but rather
“rushing to judge something useless is a very noisy predictor of actual uselessness”
It probably started all the way back in high school with people in the back of the class asking how all this high school maths would help them in real life. Then you get to university and people ask the same in just about every class. Then you get to industry and all the people who had that attitude growing up are calling you for help (and the people who still have that attitude seem to stop learning, or learn at much lower velocity).
It’s always more obvious in hindsight, and particularly with maths: stuff always seems kinda useless before you deeply understand it. That’s unfortunate, because it severely hampers the motivation to learn the stuff in the first place… But it is what it is, I guess.
Even pure mathematicians, who have every incentive to see their own work as immensely useful, are notorious for frequently having no idea just how useful and applicable their work will be in the future (albeit usually over longer time horizons).
My experience is that this is even more true for cross-disciplinary applications, as either discipline naturally is unaware of the perspective of the other discipline. It’s true that it’s important/necessary to specialize deeply and narrowly, but the value of cross-disciplinary skills (especially regarding maths) is probably under-appreciated, IMO.
Outside of game programming, topology isn't useful knowledge for software engineering. A clear exception to your rule above.
Being an strict adherent to a heuristic and not examining the specifics of a situation is in my opinion a poor habit. Superficially pattern matching will lead people down the wrong path more often.
I haven't found any utility to the CT that is above the scope of Haskell; it feels like if it's too advanced to implement in Haskell, it's too advanced to find a use case anywhere.