I don't think normies actually care about the soy content of the movies they are served. That's just the loud minority SJW crowd. Normies care about Chad/Stacy actors, explosions, and comedy. See how Ghostbusters 2016 which tried to appeal to SJWs too much did at the box office.
Also, even amongst the 'woke leftists' there's a divide on what's actually 'progressive'. Take the recent anime 'Ishuzoku Reviewers'. The 'sex-positive' crowd would see it as depicting sex-workers positively, while the crowd that thinks all prostitution and pornography is patriarchal oppression is seething over it.
Also anime isn't exactly blackpilled, a lot of it is otaku cope depicting the perfect waifus that the writer made to be relatable to him, hence 40kg girls sword-fighting buff 7ft guys, which happens to align with the progressive idea that females can do anything a man can.
Then there's the whole yuri/yaoi/trap thing, made mostly as a niche appeal fetish thing but some people would see it as being progressive. Traps (girls with dicks) have especially became a popular giga-cope amongst the tranny community, who see it as validating their idea that guys can turn into girls. This is how weebs got their association with faggotry.
There's still the loli themes that draw western ire, but that imo won't be enough to kill anime over. Besides, the whole muh 17.9 years old toddlers pedo panic thing is a major normalfag cope when most men find teenagers attractive and most teenage girls are having sex.
