Anime/manga seems safe from western SJW autism, but it does seem like Japan has its own version of it sometimes. I know serval popular mangaka they seemed to have TDS (biggest one seemed to be Yusuke Murata but I think that lasted less then a year) and I know their are some shitty woke series because shitty woke scanlators go hunting for them. There isn't much but you can find a few sites like pixiv or online magazines, last one I saw was some kind of tranny hunter one shot but can't remember what it was called.
As for western influences, all that maters is sales and based on industry reports it seems mixed
Based on a report from 2020, overseas revenue does make up a large part of the total revenue at over 1.2 trillion yen, but there are two (*)
* It groups all revenue sources from overseas, (TV, movies, streaming, merchandising, etc). into one group
* It doesn't break it down between country (best it gives is breaking it down to number of "contracts" which the US had 292)