The 2010 Equality Act DOES NOT allow anyone to self-identify their sex or gender. This is a lie that Stonewall, Mermaids and others have cynically spread around the public and especially the private sector. That is how they have got organisations like the Girl Guides to admit males.
They say that when the Equality Act says discrimination against those undergoing gender reassignment is prohibited, that means that transgender people must be treated as their desired sex. That is not what is meant by that section of the law. It means trans people shouldn’t be treated differently from non-trans people of the same sex, for example, they shouldn’t be denied promotion or sacked due to transitioning. The exception is those trans people who hold a GRC.
It envisaged that trans people with a GRC would usually be treated according to their legal sex but even here exceptions can be made if proportionate and necessary to achieve a particular aim. So it would be appropriate to exclude trans women from an female-only exercise class if the aim of the class was to improve exercise rates among conservative Muslim women, who wouldn’t attend if a male started attending, especially if other exercise classes are available.