You were doing so well until the pink triangles?.
It's good to see a more rational approach, though, and I am absolutely sincere in saying that.
I think that the reason the Equalities Act is not being used effectively is because there is so much confusion as to what is 'discriminatory' because of Stonewall and other groups' vociferous objection to anything that suggests that men cannot become women at will.
Re the changing room issue - I see your point about religious women not using mixed pools (although in some centres there is more than one pool and times that are designated for different groups), but I still maintain that in a female-designated changing room it is reasonable not to expect to see a man with his tackle out - particularly when children are present. The question of whether it should be called a 'safe space' is largely one of semantics. There should, IMO, be a much more open debate about what is meant by various terms, so that they can be used in a meaningful way by all concerned.
The question of how staff would know who was a transwoman is fair; but outside of situations such as swimming pools where, with the best will in the world it is fairly obvious if someone is male, it won't matter unless someone draws attention to themselves in an obvious way. As we have been saying on these threads for ages, most women probably don't care if we sit next to a bloke in a dress, or a fully transitioned transwoman, or people at any point in between. What we are asking for is protection against men using the trans issue as a loophole to attack (literally or metaphorically) women.
Personally, I also see the change in language as a metaphorical attack, as if it continues women as a separate class will simply disappear. There will be no mechanism for counting instances of abuse, of discrimination, of criminality or all the other things that are used by policy makers. It is not about discriminating against transwomen - it is about protecting the rights of women.
Is this where we can all sit in a circle and sing Kumbaya? ?