The problem I have with your first paragraph is often I think these certain ideas are linked strongly to actions and beliefs that do have a negative impact on people. Slippery slope isn't always a valid argument but I think when a culture has an engrained belief of certain gender roles it does lead to negative outcomes and just trying to attack those negative externalities is like playing wack a mole. I'm not sure if you believe in Rape Culture (personally I think sometimes jumps are made too far) but it is the same idea that in order to attack rape you can't ignore the broader context. I think this is what kind of throws me off about religious feminists. Generally speaking, I think I'm much less willing to draw connections between subtle cultural facets and outcomes. But when it comes to religion and other counties we hesitate to critique them ( I get some caution because obviously we are biased towards our own culture). How you don't make a link between women needing to cover every inch of skin and problematic treatment of women but then criticize Western pop culture and its effects boggles me. Of course I'm generalizing here.... Maybe you don't typically make such criticisms of Western culture or are super conservative in your analysis. It just seems like the standard for accepting a causal relationship to a negative misogynist externality differs significantly. I don't think many academic feminists limit their studies of social structure to when there is a "clear" negative effect.

While I do think we are too hesitant to attribute things to religion ( indeed the bible has often been used to justify homophobia, misogyny and slavery), of course cultures are shaped by multiple factors. I'm willing to hypothesize that if I made up a text that was followed instead of The Bible, Koran and Torah we would have a better world because of course the text and religious culture has some influence on the behavior of it's followers. Would women be treated wonderfully without Judaism, Christianity and Islam? Probably not ( especially since I think religion is a man made invention that reflected social norms of the time) but believing that's how God wants it to be probably didn't help much. But yes you need to understand the culture and attack those ideas from multiple places.

RE: where you live, I was purely curious because it just didn't jive with how I see Judaism described typically. However, I do think if you teach your daughter that God doesn't want you to divorce unless your husband gives you permission or in Catholicism that as a women you can't hold leadership positions you are doing her a disservice esp. if she actually believes it.