Girl guides is a separate issue although I am not disagreeing with your point.
This is about paid for services (there is an argument GG fall into this category but this isn't what I am really talking about).
Gyms will have to advertise what they are doing. They will have to put up notices. If they decide to allow or disallow - either way they will have to make their position very clear or they run the deception/misleading risk as has occurred in the USA case above. Because the service offered in the original contract would have materially changed. If self id is introduced they will need to make this clear for all service users, whether they are trans or not. It would have to be overt otherwise mayhem will ensue.
This for them could mean big losses. Annual contracts will be null and void as the original terms have changed.
I would expect that women only gyms will see a surge in clientele as these will be the only ones that could probably maintain a proportionate exclusion. Others will struggle a bit more to justify it.