The messages that old Disney movies send to girls were a product of their time. I think the more modern Disney movies send excellent messages to girls.
https://www.theguardian.com/film/2013/may/16/disney-princess...
It seems to me that if a hyper-sexualized/glamorous Princess Collection will make 2% more profit for Disney then that's what's going to happen regardless of how many young girls feel inadequate about their looks and end up with eating disorders.
And yeah, sure, they'll kowtow for a while when there's a backlash, and maybe you'll get a plot like in Frozen about sisters who are supportive of each other. But that lags the culture by like 10-15 years and only happens when there's profit in bucking the damsel-in-distress princess tropes that Disney itself is mostly responsible for.
Maybe once they could be ahead of the game instead of patting themselves on the back for finally reversing long-standing trends of their own creation. Wouldn't it be nice to have a back catalog you could be proud of, rather than have to apologize for?
1) Old Disney - The best thing that can happen to girls is finding prince charming.
2) New Disney - Girls are just regular protagonists, sometimes purposefully going against the tropes.
3) Anime - Incredibly variety, top 5% is amazing re: girls or boys as protagonists, but a lot of it written for teenage boys and has women as side characters for sex appeal.
(edit: based on another of your comments you seem to be fully aware that there is great non-sexist non-objectifying anime out there, so your "almost any" comment is confusing. I don't know much about anime, but I've been watching some of the highest-recommended and rated films and they've all been great about this in my opinion.)
While there are certainly mature, grown-up anime with characters that make sense (try Your Name for something newer than Ghibli) a great big chunk of anime are just childish.
In my opinion anime tends to be less childish, and better done than american animation. The sexualization is a bit concerning, but I think that's just different cultural values.