Apparently random compliments about hair and make up are park of what makes us women.
I'm in my 50s, my DD is in her 20s and i have often received and been given compliments on anything from hair to nails to shoes (not always heels, sometimes docs or whatever) in a range of places including a supermarket toilet. DD and her friends, and it seems the wider generation of millenials do often complement each other on things, in all sorts of places including (from the last 2 weeks out with her): trains, bars, the street, a bus queue, a shop (not clothes), a shop (clothes), a cafe and a pub toilet. They often step out of their way to say "i really like your outfit/hair/lipstick" and i actually think it's great, it really gives both of them a lift.
My personal worry isn't transwomen in the toilets. My worry is that abusive men who want to get into women's spaces (toilets, changing rooms etc) have an open goal in legislation that says "anyone can state their identity and everyone else must accept it". That is not to say there aren't transwomen who will find this a lot easier. I just believe that if you have to work a little at getting a GRC it puts off the spontaneous idiots who would go in the ladies for a laugh without making any alteration to their appearance and when challenged have a perfectly legal defense of "but i AM a woman". I'm not sure how i feel about the hoops transwomen (and men) had/have to jump through at the moment to get a GRC but it does involve some effort to "live in the gender" for 2 years (IIRC). I can quite well believe that having to do this for 2 years seems onerous to someone who have finally accepted that they are transgender and not losing their mind, but i prefer that to a sudden change which can have serious repurcussions for everyone.
It is very difficult, however, to accept that this legislation will basically imprison some women, who have fought long and hard to be allowed to mix with other women, because their culture/religion/controlling family now won't allow them out on the offchance they share a space with a transwoman. That is unacceptable. Making women who don't have those restrictions uncomfortable is also unacceptable, tbh, and i would prefer sex segrated fcilities as well as gender free ones.
One thing that really fucking boils my piss though. Is being in a long freaking queue for the ladies which is populated with boys who are old enough to go to the toilet by themselves. As soon as they can unzip, pee, shake, zip up and wash their hands they should go in the men's. I reserve my especial ire for those boys in the ever increasing long queue for the ladies whose dads then come and stand chatting while they wait having whizzed in and out of the men's toilet which has a tiny line (pun intended)
So all in all I'm conflicted. People going in, using the facilities, and going out again - not much problem. Including men (eg at a Rush or neil Young gig where the audience is 90% men). Opportunists who might use current thinking to harass women in their spaces? get in the sea.