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I'm sure you would agree that a man with long hair or whatever should be called 'he', so I also don't see why that doesn't extend to transgender men for example.
As for neopronouns like 'zir', I don't think I ever actually encountered anyone who uses them, either online or irl, with the exception of one Twitter user who preferred 'it'. So I mostly see them as a non-issue, although if someone does prefer a neopronoun I don't see the point of making a fuss either.
Humans have been able to handle this sort of thing long before 'woke' was ever a thing: name changes due to marriage, or social pressure or immigration, or title changes like Miss/Ms. becoming Mrs.
It may be helpful to remember that the "ask" of you is a minuscule amount of effort compared to the person making the ask, who has probably agonized and struggled with their identity, their relationships, and what sort of repercussions they may face when they ask others to change how they refer to them.
Yes. Therefore by that convention:
> calling for instance a transgender woman 'he'
is entirely reasonable, because "transgender women" are, by definition, of the male sex.
If you don't agree with that, maybe this article will provide some food for thought: https://fairplayforwomen.com/pronouns