As for Eddie Izzard she was dressed as a woman, she identifies as a woman, woman is a social construct and so she uses the facilities provided for the use of people who comply with the social construct that is woman.
So dressing and identifying as a 'construct' makes you become it? I'm guessing that duchesses are social constructs? I quite fancy being one, and I have a posh frock upstairs. Does this mean that I get to use the VIP lounge from now on? Just call me Your Grace.
You are entitled to believe those facilities are provided for the female sex, which is different, but quite how that will be policed or the restrictions applied I have no idea. I tend not to favour laws and rules which are unenforceable.
Well yes, that is different. Me being a duchess is a fantasy, but me being a woman is a biological reality. As for the policing thing - I tend to favour laws and rules that make sense and benefit society. The police and lawyers can work out how to make people comply. That's not my area of expertise at all, but it is theirs, so I'd happily leave them to it. Or the Nudge Unit would be able to sort it in no time, I expect.