I wouldn’t care that much either if this was just about pronoun use in their presence for the purposes of conversation, but “trans people” want pronoun enforcement even in contexts for which we are not present, and they want it regardless of how credible their professed gender identity is.
Not all, but some do, and this is the legal reality in Canada, where a guy with a very male name and presentation was able to sue woman-only aestheticians for refusing to wax his balls, and to a lesser extent in the UK, where until recently people could be fired for stating that they don’t believe you can change sex (still the reality in the USA, although to be fair our employment laws suck in general).
Since they’re the ones that tried to weaponize the law against the people that didn’t want to play along, it really is everyone’s business, and I am definitely bothered enough by it to care.