So let's poke this analogy further. Standard titles (which are inherently sexist, by the way) hold that you call someone Miss if they are unmarried and Mrs if they are married. If a Miss gets married, you now refer to them as Mrs. And (in the standard heteronormative patriarchal paradigm) she will frequently change her surname. There's no question about which title to use. Except that now she wants you to call her Ms. as she does not feel that whether she is married or not is relevant. And you do so. You don't quibble over what Ms refers to. You just use it because she asked you to.
Yes, let's. Because I also happen to know that nobody normal actually thinks it's painful or bigoted or anything if they've been called by the wrong title.
One of mom's stories is how a couple of classmates decided to call her Miss Mustermann (or rather the local i18n version of it) after she got married in college. That is the combination of Miss and the family name she got from her husband. She just found it funny.
Or I've been misgendered before. The last time actually on work chat. In fact, he actually distorted my name into a girl name. Couldn't care less.
As I was saying, it seems to me like those demanding that I treat it as 100% certainty and perfectly logical, or it's painful for them, are just telling me that they don't seem to be that certain themselves. If everyone has to walk on eggshells around it, lest it starts feeling painful, that uncomfortable sensation is just what cognitive dissonance feels. And it means it's actually a very wobbly and unsupported part of their mental model.
Seriously, if you have something that you either feel perfectly justified to believe (e.g., I'm a programmer because that's by definition what me being employed to write programs means) or that you don't feel like it needs any particular justification (e.g., I like burgundy, as in, the #800020 colour) you don't need everyone else to validate it. Meaning you have no reason to be triggered by it if someone doesn't. If someone says "no, you don't actually like burgundy", then they're just crazy. They have no way to know what's actually in your head. So why would you care?
So, anyway, far from me to tell them that they can't still go for that mental model, BUT -- and this is a big fat BUT -- if they're not all that sure themselves that it's not just some counter-factual belief, then why is it an obligation for everyone else to act as if it's absolute truth? Doesn't it boil down to a bit of hypocrisy?