I first encountered them on a channel called Disparu (reviews of modern TV shows). In his case, I don't mind the overlay, but it's the obnoxious clicking sound that drives me crazy, especially if I'm just listening and it's in the middle of the video.
Similar to what Piroko mentioned, the Persona games (well, from 3 onward at least) attract leftists. It's similar to Danganronpa games. Any discourse on characters immediately leads to "<character> is trans/gay/bi" or "<story event> is problematic." It's unfortunate, because the Persona games are very good JRPGs.
I'm almost inclined to say that it's because the "idyllic school setting" attracts them because they had such terrible experiences... But that doesn't explain Danganronpa.
I think this is better than just replacing Vic and Karen, in my opinion. Better they change everyone than just the controversial ones. (They also haven't had Fuuka's original VA since P3 Portable, and I don't think Wendee Lee fits the character...) I won't hold my breath for soundalikes, though.
In general, modern anime (and manga) isn't woke. If there is something woke in one, it usually the fault of the translator as you noted. A recent issue appears to be turning traps into trans, despite the fact that the original doesn't do so.
Comic books in America traditionally catered to young men, but manga in Japan is divided into several different groupings (for boys, girls, and so on). Of course, there are some that do try to appeal to wider audience even if labeled for a specific one.
As others have mentioned, you can find interesting anime/manga even with premises that sound uninteresting. (I really enjoyed one about the board game "Go" when I was younger, for example.)
There are many, many sites you can use for watching anime that aren't official but (I believe) are generally safe. I use 9anime with an ad blocker, but you can find a host of (generally) safe ones on Reddit.
Getting offended by this is like being offended by "Cofagrigus" (a Pokemon) having "fag" in it. How do these people even live when they view words through a video game filter?