What about the young person I met who looked like a girl but chose when asked to identify as "they" have 'they' no right to do that?
Yes, IMO anyone has a right to ask to be addressed as 'they', and I have no problem with addressing people as such* if that is what they prefer. Where I disagree is when everyone is asked to make a statement by choosing a pronoun, which has happened in requests from HR to at least two people (working in different companies) of my acquaintance.
As regards toilets, it is not so bad if there are cubicles with floor to ceiling doors, but they are rare in public loos for safety reasons. Cubicles with gaps at top and bottom afford little privacy when they are unisex - anyone can peer over or under the door, stick a phone under or over and take a photo.
Regardless of the style of the door, if cubicles are all in the same area, behind the same entrance door, there is no reason why a man lurking around would stand out, in the way that he would in a female-only block. I have known several women who have been assaulted by men following them to the loo in pubs and clubs over the years (one very seriously), and am not at all happy with the idea of unisex loos, particularly on licensed premises. It is not remotely the same as sharing bathrooms in the home.
*Except that people aren't addressed as 'they', are they? It would only be if someone were being discussed that a third person pronoun would be used, and then usually in their absence. Nine time out of ten, people are addressed as 'you', or by their name. When everyone in a large company is asked to choose a pronoun, the only way people will remember which one to use is to look it up each time, which will, if anything, draw attention to those who choose 'they', as they are likely to be in a minority unless it becomes politically undesirable to use gender-specific pronouns, and wipe women out altogether.