I think the heart of the dispute is about the grounds on which the measurement can be corrected, rather than changed. Mistakes can always be made so the sex assigned at birth could simply be wrong, in which case it can be corrected. But are someone's subjective thoughts and feelings sufficient to correct it, if the objective measurement still gives the same answer?
Well, the dispute was about whether it should be possible to change your legal sex
at all. If you think you should be able to change your legal sex with a note from your doctor, you've already strayed significantly from the
scientific truth. The relevant fact there is "do you have gender dysphoria" and not "are you the sex you would like to be legally recognized as". Most people who oppose self-id seem to be ok, or at least more ok, with that situation, because they're concerned about the potentially destructive
outcomes of permitting self-id to a greater degree than they are about having legal definitions
be scientific definitions. There's a tacit acknowledgement that the public reason can result in a different definition because there's a different set of justifications at work. And that's exactly the problem with the lunatic fringes--they don't respect that fact, don't acknowledge that we need shared ground, and won't give an inch. A definition works if we can all live with it and it leads to better outcomes, but not if it leads to bad outcomes. And even thoughtful, rational, evidence-seeking people don't agree on what
counts as a good or bad social outcome, so there's necessarily some negotiation involved.
Meanwhile, science (and to at least some degree medicine) isn't really about
social outcomes per se. It's about describing things as they actually are. That's what it's good at. That's not what the law is good at, and not even what it's good for.
Personally, self-id looks like small potatoes to me, barely even different from what it generally replaces (like motivated people can't doctor shop). I was far more concerned when one of the most influential Supreme Court justices in recent history revealed that he believed that the devil exists, that he's actively working in the world to make people atheists, that demonic possessions have happened in the past, that the reason they don't happen any more is because the devil got smarter and sneakier, and when confronted with the merest hint of skepticism, took grave offense and pointed out that his interlocutor was out of step with the American public. And then there were his
legal ideas....