Interesting that you picked a female wanting to be known as male as your example. As we all know, being male doesn't officially qualify you for much (unofficially of course, it qualifies you to all the privileges that the structural and unconscious biases of a system and culture shaped around male norms affords, but being implicit and in many ways not even conscious, a female person doesn't gain access to those just because she adopts (her idea of) a male identity). So you, deliberately or unconsciously, picked the most innocuous version of an assumed identity as your counter example.
Let's pick the more meaningful scenario where Paul at work wants to be called Sarah. That's fine, right? Only an inflammatory arse would engage in the spectacular waste of time of objecting. So Paul is now Sarah.
What happens when Paul wants to join the women's mentoring circle. Everyone apparently "accepts" (because they didn;t make a fuss about) Paul as a woman called Sarah now, right? So it's very hard to object to Paul joining the mentoring circle. The young women in the circle want to be kind and welcome Sarah. But they don't feel quite as comfortable talking as they did before. And Paul, even though he's trying to be "one of the girls" - well he just doesn't have the same experiences as they do and doesn't understand why they don't just promote themselves better.
And that prestigious industry conference looking for female speakers? Should we propose Paul? He has a great story, and it might look bad if we send someone else, might look like we don't really accept Paul as Sarah. So Paul gets a fantastic opportunity to build his professional profile internally and externally off the back of women's support.
Just a couple of examples to show you how accepting that a man can qualify as a woman means more than just being nice to Paul by calling him Sarah and avoiding mentioning he is a man.
But perhaps you think caring about women's opportunities is itself a spectacular waste of time.
So where is your line? Do you accept Paul as Sarah in name, but stop him participating as a woman in other ways which will hurt him just as much, maybe more, or do you go all in and open up everything aimed at women to Paul's version of womanhood even though it makes the supports that are supposedly there to support women no longer fit for purpose?