Oh hello OP! Great follow up post! Really helpful of you to prove so very clearly that you don't actually care either way about what Muslim women might want, you just wanted to bitch about women who want single sex spaces and thought stirring up a nice bit of Islamophobia would give you an opener.
So, on to this new topic.
Among the many things you are missing is that even this single letter writer (whose voice weirdly seems to have more weight with you than the many many women who disagree with you) doesn't use men's toilets exclusively, but occasionally, from time to time, when it's convenient for her, and most importantly at the time, and the venue, and with the men, of her choosing.
If there hadn't been a queue for the ladies do you really think she would have been squatting over a urinal?
If she'd walked in and there was shit all over the stall would she have pee'd anyway?
If she'd walked in and instead of saying "fine" and looking away a bit embarrassed, one of the blokes had reacted aggressively or sexually would she have carried on?
I don't think so. I think she'd have turned around and gone straight back out again to queue for the ladies. Because she has the choice.
And choosing to use mixed-sex facilities (which as I'm sure you know means more than toilets) when it works for you and you can decide if you feel safe, or comfortable, or unembarassed, is very different to having no choice about it ever, to never being able to get away from men no matter how they behave to you or in that shared space.
But you knew that, right?