I can only imagine that women only groups are not permitted because the women would join them, leaving all the men alone in the inclusive mixed sex group. We can't have that because then there's no one to "validate" the members' "womanliness".
As for the staff...from what I've heard of those in Brighton, they are twaw. They believe they are being #kind to the #MostOppressed and we're just evil bigots. It's a religious movement and they are doing the work of gender Jesus, converting or casting out the ignorant masses as required.
Reading The Righteous Mind by Jonathan Haidt helped me better understand these people on an intellectual level. That said I think they're completely wrong and I struggle to comprehend HOW anyone can hold such a radical and nonsensical position and keep a straight face.