I overall agree that for some things it can make sense to have separate gendered spaces, shelters make sense, I can see gyms, etc. places where people are feeling particularly vulnerable, self conscious, dealing with trauma, etc. and being around the opposite gender could be a part of that.

But in other cases, I think the right move is to get over ourselves and be rid of pointless gendering in some activities.

A lot of my friends and myself are traditionally "manly" in a lot of ways, outdoorsy, cigar smokers, whiskey drinkers, a lot of us work with our hands, like guns, etc. That said, we're a pretty enlightened group, we're not out shit-talking our wives and engaging in demeaning "locker room" talk and such when we get together to have what could be loosely called our "boys nights out." It's happened from time to time that a female friend ends up tagging along and absolutely nothing changes about our behavior, the fact that there is a woman in the room in no way takes away from the experience, and if anything adds to it in a "the more the merrier" sort of way. Any woman who is willing to put up with the cigar smoke, fart jokes, peeing on trees in the woods, etc. is more than welcome to come along, it just happens that most don't enjoy that.

Now of course you also run into a whole lot of complicated situations, the way men tend to interact with other men, and the way women interact with other women are different. I'm not going to go into all of the nature vs nurture, societal expectations, toxic masculinity, etc. involved but all of that certainly plays a big part. I'm no sociologist, but my overall impression (and I may be wrong)is that women can kind of mesh into the male social structure without making too many waves provided that the men aren't assholes (which is far from guaranteed,) but it's very hard for a lot of men to get themselves into the right kind of headspace to participate in the sort of socializing women want and need from their social groups without disrupting things to the point that the women aren't able to get what they need out of it.

And circling around to shelters, men may need more shelters by sheer numbers, but on average each individual homeless woman is probably in a more vulnerable position than the average homeless man. Really more shelter space is needed across the board.