Maybe a solution is to properly seperate sex and gender, since they're different things. Make up some new words rather than having the same words for both sex and gender.
Because they are separate things only for a small percentage of the population.
For the rest of us, the majority of people on the planet, Man/Woman and Male/Female are
exactly the same thing or at least interchangeable and we don't have to pander to the minority who want to force the rest of the world to use their newly defined terminology. If
they want to use new words while talking about their problems, all good, but they are not going to force the rest of us to comply with their subjective needs for validation that go entirely against the norms the rest of us live with.
Using hyperbole like 'denying existence' and claiming 'hate' or 'bigotry' when people are more likely mildly annoyed or ambivalent is just manipulative and should be called out as such. I don't
hate anybody - not even the person who nearly killed me when I was a teenager and if I don't have any hate for them you can be damned sure a man in a dress doesn't get to lay claim to my hate either.
If someone want's to present themselves as the opposite gender to that which matches the biological sex they were born with, that's fine, I have no issue with that. Live and let live I say. However if they then want
me to pretend along with them that they are not gender that matches their biology, then depending on the circumstances, that's going to be a big fat no. To clarify my comment about the circumstances, it will be a 'yes' to be civil, polite, kind, etc. in general day-to-day life, and I'll use their preferred gender pronouns (unless it's this Xir/Xe nonsense) in conversation. But get into a rational debate and it's back to no and when males start taking things away from females (like medals) it's an even firmer NO.