They don't need to investigate or demand any evidence when they already know sex at at birth
No, they don't. What the teacher knows is that X is their student and goes by "she". Nothing further is known. What is guessed or assumed doesn't
matter because
and are being asked to participate in the process of social transition
they are
not "being asked to" do anything other than engage in the common courtesy of taking someone's stated preference for being addressed into account. Again, they aren't the Sex Pope issuing official edicts to declare X is a particular sex. All that's being asked is to not
argue with X on a matter which is
none of anybody's else's business anyway.
This is all true, but it doesn't tell us why teachers ought to be compelled to help their students change sex.
If you believe telling someone they use a particular pronoun is the same as "compelling them to help them change sex" then you clearly believe, ancient Egyptian style, in the magical powers of words. In which case you really ought to be on the side of "words = violence"; if I can change your sex by uttering a syllable then imagine what else my powers can do!
And yet you want them to be required (by law or policy) to aid in the process of transition from female to male, or vice-versa.
Again, no. I want people to mind their own business and exercise the very basic and reasonable courtesy of not challenging people on what sex they are.
It's only a battle is you assume someone has to prevail, as you clearly do.
You're the one who said "two sets of stated preferences come into conflict". I think the stated preference of a person to be referred to by a particular pronoun is the only preference that matters, as it is basic courtesy. If a professor for some reason feels called upon to act as Champion of Sexual Truth and challenge them, well, I have zero regard for that sort of unprofessional, rude, and quite possibly
literally insane point of view. "I think my student, Shelly, has or had a penis at some point!" is an idea they can keep to themselves, or gossip with to someone else. It's certainly not appropriate, acceptable, or welcome for them to express that to Shelly or her classmates and start a fight about it.