[candy_coated_bitch]

I'm not an EXPERT on Japanese anime, but I do know some about it. Mainly from people I know who are obsessed LOL. I am answering with that caveat.

The shows you are describing sound pretty obnoxious and sexist. I think maybe the best you could do is explain to her why you think those shows are sexist and not particularly empowering to girls. You sound like you've started doing that already. In my opinion you should absolutely have conversations with her about it and not treat it as a "phase". It may very well be a phase, but she's also getting messages there at the same time, you know? Maybe not make it into a huge, dramatic thing but start a dialogue. Maybe ask her what she enjoys about these shows so you have a better understanding of why she's watching them

And as traumaqueen and dykeumentary have said: there is a HUGE range of stuff out there. From the type of stuff your daughter watches, which may not be terrible positive, to stuff that depicts women in girls in much more positive light, to stuff that I think would be HUGELY inappropriate for someone of her age. It's like anything else I suppose.

I'd say just open up some conversations and see what's going on there for her, as a starting point.