Possibly you've noticed that there are people who are going around using terms like "cis" and think that words like woman or man refer to something they call gender, rather than sex.
That's a disagreement about the meaning of what those words mean and how they relate to sex.
I'm really not sure how you would claim that no such controversy exists, it's what the thread is about. Unless you have some totally different definition of "false" or "verifiably."
Other people are allowed to have beliefs and ideas about other people that you do not agree with. They are allowed to think that you have a soul, or are oppressed by the patriarchy, or your aura needs to be cleaned, or that you might have been injected with nanobots when you were vaccinated, or any other idea plausible or implausible. They are also allowed to think that you, and every other person around, has a gender identity.
Other people are allowed to speak about the world, and other people, in a way that reflects what they believe is the nature of reality.
As soon as you start telling people they cannot speak about what they think is reality, you are in a very dangerous position. Do you really not think there could ever be a time when what you think is real is seen as wrong, regressive, and even deeply offensive? You can't maybe stretch yourself to think of any recent examples of that kind of thing.
I am pretty disgusted to be honest that after the years here of making arguments about the necessity for people to be able to speak the truth as they see it, and the fat that people who disagree and feel threaded or offended about it need to suck it up and be adults, as soon as the tables are turned even a little bit they revert to language control and trying to force people to accept the new dominant narrative.
I had rather hoped that many women who had considered themselves on the left had had their eyes opened to that particular failing, which would make for a much stronger political culture going forward, but I guess not.