Well, thank you Nitronine. I have been lurking here rapt in admiration for the brains engaged in this issue, so I appreciated that comment.
Any new wave refuges etc would have to be set up with unbreakable legal protection, like the private men's clubs, Garrick etc, to avoid PCSOs rolling up at the door claiming it wasn't appropriate to be single sex.
And with regard to that PCSO, someone has mentioned the JWs, and her certainty that what she "knows" (not believes) is right is like theirs. She hasn't just been on a couple of courses. The JWs maintain what they "know" with multiple meetings each week, they swim in a sea of it, they don't have a chance to know anything different. If someone tries to persuade them that their reasons for rejecting all other churches do nt apply to the Quakers, for example, they will fall back on the Watchtower organisation having done their research, and the Quakers are definitely wrong. (Meeting House next the KIngdom Hall - interesting. They are forbidden to take other people's leaflets.)
No debate obviously leads the same way.
That PCSO seems to have been indoctrinated to that sort of level - that needs investigating.
My houseshare, whose reaction to the nearly daily exposure to horror stories from here is admirable, is of the opinion that what is behind all this is someone's psychological warfare department. And/or PIE. He recalls the denial of debate technique used against him in the past, in a not entirely unconnected context, decades ago.
And the first thing the instigators have to do, of course, is to turn the idea of conspiracy into something laughable.