I haven't read the full thread, but I had to post in response to this, as I find this attitude bewilderingly illogical/naive. Safeguarding is about reducing risk. The stats - and sheer common sense! - are very clear that single sex spaces achieve this. Any argument that predators can already access these spaces anyway shows a total disregard of this basic principle.
Until recently, if a set of loos was isolated, a - probably the, in fact - key factor influencing my decision on whether or not to use them would be who else was in the vicinity.
From my young teens, using an unpleasantly lonely & claustrophobic set of ladies' loos at the local cinema mid-film, I'd always, very consciously, look across the vast, empty foyer to make eye contact with the people behind the popcorn counter so they noticed me going in, safe in the blessed certainty (back in those halcyon days) that if a man were to then follow me in, they'd be on it, instantly, metaphorical alarm bells ringing.
Now?
Any man could follow that 13-year-old girl through the door into that long, lonely corridor and claustrophobic room at the far end, and staff wouldn't think twice, or dare to comment.
So, now, I wouldn't use those loos.