There is a need.... as you brought up "equality". And if you are ever going to use that one again, it would help to show how it is not already "equal".
Single- sex spaces, are just that, for a reason. Nobody cares what gender anyone is, as that actually doesn't mean a threat, but sex differences too.
I am not "self-entitled" to prefer to get undressdled away from strange men. You wouldn't understand, but it is not unusual for women to feel more comfortable away from them.
Why should I feel uncomfortable or anxious, because of someone else's sense of self- entitlement (which they are not actually entitled to...)
And what is wrong with them just using their own places, anyway?