@CloudyVanilla
My understanding is that any service provider can deny service to a trans gender person if (there is a specific phrase I can't remember) but basically if it impinges on the single sex users (as in the women if it's a women's service and men if it's a mens).
So if for example a trans woman is causing no problem and is legitimately/in good faith accessing a service then the provider can allow that. If a trans woman accessed a service and was being creepy/insincere in their motivation by being there then they have every right to remove them.
This is a misunderstanding of Schedule 3, Part 7 (Single-sex services) of the Equality Act.
First, a provider has to have a reason to offer a single-sex service, facility or space. From this, the provider can exclude all members of the opposite sex if this is a reasonable means towards a legitimate aim. This includes all people of the opposite sex who identify as trans.
If the latter are legally of the opposite sex through a GRC, the provider can still exclude them. Most of the time, the reason why something is single-sex in the first place, is sufficient to justify their exclusion.
However, since the Equality Act was first enacted in 2010, providers, businesses and public bodies have been erroneously advised that they should not exclude people who identify as trans from opposite-sex provisions and must not exclude people who identify as trans and who have a GRC. This has shaped policies over the last decade, to our detriment, but that is not the law.
Which is what various campaigners have managed to get the EHRC to concede in a public statement made in 2018, but their erroneous advice remains in place. Hence Ann Sinnott is seeking a judicial review to compel the EHRC to issue not only correct guidance, but also inform all organisations and businesses publicly that they were wrongly advised by the EHRC.
Also, just to clarify any provider has the right to remove any person from their premises on grounds of that person violating the rules of conduct. This is regardless of sex, so a female person can be removed from a female-only service if she harasses other customers or damages the premises. The same goes for mixed-sex settings.
tl;dr: The sex-based exemptions apply regardless of behaviour. The sole deciding factor for exclusion is a person's sex (either biological or legal).