I'll start by confessing I'm on the wrong side of this fence.
I once stopped shopping at a very popular chain store (let's say one of the Nordstorms of India?) for half a decade precisely because my husband was shooed out of the lady's lingerie section where he was helping me choose stuff at one of their flagship stores. Another lady out shopping with her daughter for the teen's bras told him he shouldn't be there just as her husband was not (!)--- and mind you, this was not in the dressing room, it was in the lingerie section, well outside the dressing room.
I was especially infuriated at her attitude that even the girl's own father needed to be banished from the area lest he observe his own daughter's underwear. Geez Louise! It was always my father who took me lingerie shopping when he was home, and when he went away on a voyage, one of the things I *knew* he'd be bringing back was undergarments for me! A woman who can't trust her partner's sexual instincts with respect to their own daughter ought not to stay with him!
I agree with much of what Rae's said, and out of genuine curiosity would like to know: What exactly does your discomfort stem from, ladies? I can understand fear of Peeping Toms --- but there Thomasinas at it too! If it's just an issue of privacy, that's what the doors and curtains are for! And surely who other people let into their personal/private spaces is *their* business? It's quite a different matter if you're holding up the queue by making out in the changing room, but I doubt that's what most people are encountering with couples or parents
Personally, I'll also note that I find men's dressing rooms are often less crowded than women's --- and I've often taken advantage of this by asking an SA if I can just try something on in the men's area if it's empty. I'm usually accommodated.
Restroom issues: I'm all for unisex restrooms if we can only help men and women and indeed any other gender behave in a more polite, considerate way with each other. I always understood 'safety' and 'shame' to be the logic of segregation --- and honestly am not at all happy about it! Indeed, I suspect the way to get more consideration and mutual understanding or respect IS to drop the segregating walls as far as possible!
As it is, I keep wondering where anyone not identifying as a gent or a lady is supposed to go --- and what if they're told it's no place for them? (Those interested should google this; someone was actually BEATEN UP by a pair of young women at a McDonald's over precisely this issue. Horrific!) I also feel awful for parents out with a child of the opposite gender who needs a restroom --- what if the child needs help? If safety is the reason to segregate, how scary must it feel to let your little one go in alone amongst the strangers that you yourself want barred from your own hygiene spaces? The mind boggles.
Alright, I'm done. Sorry for the rant. Also apologies for stepping on your toes, ladies. But I do think it is rather important to explore the source of this discomfort and its validity, even if not on this forum. It's holding us (and them) back, I do fear.