Maybe the OP's problem is that she's not a man.
As a man, I think it's very generous of you to say that I should be able to demand the right to be "treated in every aspect as a woman", but it's mind-bogglingly naive. Okay, you may never have seen inside a man's head, but, seriously, don't you know what men are like?
I may be a lovely man (obviously, cos I'm Nick Cave), but if you're letting me in you're letting in every other man.
I'll gladly take any special funding you have, and accept a place in a "female" prison, if it's as simple as ticking an "F" box. Why not?
The only reason I wouldn't would be a wish to avoid upsetting women - but in a situation where any man can do it, I'd be a fool not to, and it's probably best that as many men as possible do it to try to end the policy sooner rather than later. I could reconcile it with my conscience that way.
The thing is, we're at the stage where "self-ID" has only very recently happened, and men have only even more recently seen that it's happened.
We're in a very small window where the take-up is still somewhat small, but rapidly increasing. In some places like California, very sizeable proportions of the male sex offender population have applied to be moved to "female" prisons.
Some organisations are suddenly trying to figure out how to stop any man just having a go at female power-lifting, and realising they can't. The increase in men claiming to be women is compelling organisations to rework their rules - even org like World Athletics that never reached self-ID have had enough problems to move in totally the opposite direction.
Lack of awareness of self-ID is the only reason it hasn't already imploded, and in places where there is wider awareness, it is in the process of imploding.
Once men realise that "F" is just an arbitrary meaningless thing on a form that lets them get a cushy time, they'll tick it. Why wouldn't I, if it doesn't mean anything? If you're not asking for my sex, why should I tell you my sex?