Well they could have had it all, couldn't they?
Legal recognition (a certificate, an acquired gender marker on their ID)
Protection from discrimination
All of the sex-based rights of their own sex and the human rights of both sexes
Privacy rights, to the extent compatible with sex-based rights
It could have worked. People are very open to the metaphysical, and could have easily coped with, say, a person who is socially female but legally male. And it wouldn't matter who passed, or had surgery
But then they had to spoil it all by saying something stupid like 'I'm a biological woman and I want my women's sex-based rights' (quick reminder - the sex-based rights are the ones that arise from actual biology, with only one notable exception - and guess whom that exception benefits!)
You'd think they'd smell a rat when it turned out that a man who 'transitions' got pregnancy and maternity rights, but could still keep his hereditary peerage, wouldn't you? 🙄