One thing that has always bothered me is how people say that ideas from category theory can be useful while writing Haskell code. It's technically true, but really only the most basic ideas — things which would be in the first chapter of a textbook on category theory, and which many might not even consider to be part of category theory itself. (For example, every type in Haskell is inhabited, which alone somewhat limits what you can say about it...)

And then there is also the fact that there is a huge difference between the skills and ideas that are useful for writing proofs in a theorem prover and those that are useful for writing quality software.

Also, anything having to do with homotopy type theory is even further removed from programming than regular type theory. Correct me if I'm wrong but I think that it is really only useful for helping prove theorems in homotopy theory, rather than being more generally useful for other kinds of math.