I suspect part of the real reason why the modesty trend has caught on (though not in all communities around the world) isn’t just because of religious influence but because they’re that fed up with objectification (I think even a pop star would realise this once she matures/changes). As for the religious influence, keep in mind the Abrahamic religions tend to regard female immodesty and nudity with utter abhorrence and disgust that female nudity in their minds are inevitably linked to malevolence, decadence and witchcraft.
Whatever the belief/ideology, they arrive at the same conclusion. If you’re constantly bombarded with nude or scantily clad female images that it’s going to necessitate some counter-reaction to this. It can be rooted in feminism but also in conservative religion. Comes to think of it, there has to be a reason why female modesty became so heavily treasured in those if because it gets tiring seeing all those naked women around. (I swear, nudity in art only happened more often after paganism due to secularism.)
Whatever the ideology, the demand for female modesty’s going to happen as a much needed relief.