If two people need to find a suitable solution to a problem then there has to be some give and take. There has to be some way of finding a position that might not entirely satisfy either, but which goes someway to solving the problem. The very first step is agreeing what the problem is in the first place. To reach agreement on the basic facts and then move on.
The basic fact of the matter is this. That some people's concept of their gender is different to their biological sex.
I've floated the idea before that this needs to be treated (societally) the same way we treat religious ideas that we don't acknowledge as being valid.
Society has managed to find a balance there. Not sure why the same can't be achieved here.
Just to name a few examples (and I'll spread them out over various religious ideologies to make it clear that I'm not "picking on" any particular religious ideology, just merely using it as an example)
Certain denominations of Christianity, Hinduism, and Judaism have restrictions on what can and can't be consumed. And have viewpoints that contrast with what we know, scientifically, about biology.
They're all allowed to practice their ideologies on an individual level, but we don't demand that every restaurant abstain from serving beef or pork, and we don't demand that doctors and biologists acknowledge the possibility of virgins getting pregnant and giving birth, and we don't demand that mortuary schools teach their students that a person who's dead for 3 days can come back to life.
People who subscribe to those ideologies can still gel with society due to a little thing we call tolerance. Tolerance is a great concept. It means I can keep my views, you can keep yours, and as long as neither of us infringe on the other or disrupt each other's lives in any significant way, we're golden.
When "requesting tolerance" morphs into "imposition", that's when problems arise. For instance, nobody has a problem with Jewish people and Muslims opting not to eat pork, and it's understood that most of our society doesn't agree with their view on that, so if they wish to adhere to that, the onus is on them to seek our restaurants that will accommodate that request. However, if there were a movement to impose the restriction on every restaurant in the country not to serve ham or bacon because doing so would make potential Jewish/Muslim customers uncomfortable (at the expense of everyone else), or to make everyone else modify their speech and proclaim "bacon is bad" (even if they didn't really feel that way) then people would have a problem with it.