I don't think women in general will stop going out. Men have always been iffy towards us and we still go out. Younger women and older girls in particular want to get out into the world and experience it and doing this exposes them to risks already, I think it's wrong to underestimate the drive that you have when you're young to "do stuff".
This will simply be added to the list of things that we have to "protect ourselves" around. Going to to toilets in a gang is already a thing, it will become universal, or if you're with a bloke getting him to wait right outside maybe. Or even come in with you! Yes that would be fine now wouldn't it. Changing rooms ditto, taking it in turns with a friend posted outside the curtain.
We can and do put up with a lot of shit already - #metoo shows that - we are used to it which is why I think a lot of women are meh.
Women from certain religious communities, women from very protective households, women who have had certain experiences, these women may restrict their lives, however lots of women already restrict their lives for these reasons so I don't see much difference.
I think that if and when women's spaces are opened up to men we will deal with it quietly, as we do with everything else, unfortunately.
I do think that the areas most likely to cause public outcry are sports and prisons.
Bottom line is sex offences at the "lower" end, harassment and intimidation of women and girls in public is already extremely common, this extends opportunity but really we're expected to put up and shut up in the main aren't we?