AuroraSaab
Squire
No I wouldn't. The Equality Act is a symbolically important but flawed piece of legislation - the exemptions are crucial. The Gender Recognition Act means that there are two ways to be a woman (or a man) for legal purposes - being born female (allowing for the variation @swansonj recognises in how that is defined) and achieving recognition through the Act. The second is what you might call a legal fiction. It matters that there are criteria for this, but it doesn't seem to me to be obvious that medical gatekeeping is the appropriate one. This, if I'm not mistaken, is how the latest explosion of this row began.
If there is no gate-keeping at all though, then 'Woman' is redefined as a feeling in your head, which doesn't reflect the material reality of a world in which women are oppressed because of their biological sex, not because of their gender identity. It would be unacceptable for someone to define themselves as black if they weren't, surely.
None of this would matter of course if we lived in a world where there was no oppression on the basis of sex or race. You could self id as whatever you liked. But we don't, so until that time it's necessary to have meaningful definitions so that people in those oppressed groups can organise and campaign for their unique and specific interests. That necessitates an element of gatekeeping, and for things like race and sex, I would say biological traits are a reasonable criteria to use.