There's such a thing as respecting other peoples' preferences or quirks, even if you don't agree with them. I have friends who smoke, and no matter how much I think that smoking is outrageously dumb, I just accept that this is what they do - and the same applies to a whole range of other behaviours, too, such as religious or dietary preferences etc.

You don't have to have a particular stance on trans issues to have the common decency to use the correct pronoun. Mind you, I'm talking about reasonable things here: I am not necessarily sympathetic to wholly invented pronouns (because that doesn't come very naturally), although I think "they" is fine, and of course, it would be ridiculous if (hypothetically) a person switched pronouns every day, but in the cases I have experienced, someone communicates that they now identify as the other gender, and that's fine. Usually it's also accompanied by enough outwards changes that it's also not too hard to do; I've met trans men that I didn't know were not biological men at first.

So, idk, to me "please refer to me as man/woman in the future" sounds like a simple, easily satisfied request and getting worked up over it to me signals that one prefers emphasising their political opinion over just being decent and accomodating.