I think this is a much more legitimate question, because it moves away from “are trans people deluded (lying, pretending, etc. etc.?)” and onto the actual policy issue: how do we accommodate trans people while also protecting privacy, dignity, safety and sex-segregated settings?
I don’t think recognising trans women as women linguistically, socially or legally requires us to say that birth sex or reproductive anatomy must become irrelevant in every context. It is perfectly possible to be inclusive of trans people while also acknowledging that birth sex and anatomy can matter too. I also don’t think “everyone who says they are a woman must therefore be admitted everywhere women are” is the only possible model. Rules can take account of behaviour, safeguarding, privacy, medical transition, individual risk assessment or the particular purpose of the space.
What I object to is the framing of trans women as inherently deluded, mentally ill, dishonest or predatory, and the idea that their identity is therefore illegitimate and should be disregarded everywhere. I also think policy is moving in a very irrational and troubling direction. I don’t think there is any sound logic or good evidence to support the idea that excluding all trans women from women’s toilets would improve women’s dignity, privacy or safety.
Recognising that trans identity is real does not settle questions about language, toilets, prisons, etc. Those are separate conversations and I think they should be answered on evidence about actual risks and harms rather than by starting from the assumption that trans people are lying, deluded or illegitimate.