how did the men at Hampstead Pool justify women iDing as men not being allowed in the pool?
Cos the men wanted them excluded.
In the other case the men wanted to be included.
Afaict, the consistent rule seems to be that men get what they want.
(Although I think a lot of the practical problem is that there are enough women who will make a big deal about "inclusion" - ie giving men whatever they want - that any man demanding stuff from women can expect some backup from some women. There's no united opposition from women. Peer pressure on women is often to concede to men.
Whereas a woman trying to get into men's spaces wouldn't get much or any support from men. There generally won't be any men demanding other men be "inclusive". There's little or no peer pressure on men to concede to women.)