Depends how it's taught. As a parallel example, it should be no problem to teach about Christianity in a school context, in terms of informing pupils that this is what many people believe. The problem is when the principles of Christianity are taught as if it is truth.
Same for gender identity and trans. It should be fine to inform pupils that some people in our culture believe that everyone has a gender identity, and that they also believe that this is what defines if someone is a woman or man or, as is described within this belief system, neither. But teaching this as if it's a fact is problematic.
A sensible policy would ensure that the curriculum is agnostic to these beliefs.
Because the responses I crafted myself to someone who uses a thought experiment starting with "it should be no problem to teach about Christianity in a school context, in terms of informing pupils that this is what many people believe." were less courteous than I wanted my posted response to be. Teaching anything about religion in public schools should be considered complicated, in my opinion. You are never just "informing pupils" in a public school setting and, as an example, if you botch your lesson on 9/11 you might get a muslim kid bullied or beat up. "But I simply informed the students that all of the terrorists who attacked the WTC were muslim! it is the truth after all!"
Furthermore, I had the gut reaction that your portrayal of how gender identity is taught in public schools is likely bad, but I did't have the time to run that stuff down. So as a consolation prize I offer one of GPT 4.5's takes on your response; Specifically I asked it to identify the hypocrisy in your response. I should probably have a more nuanced prompt in this case, and I would also encourage you to have a more nuanced view of teaching religion in public school.
Same for gender identity and trans. It should be fine to inform pupils that some people in our culture believe that everyone has a gender identity, and that they also believe that this is what defines if someone is a woman or man or, as is described within this belief system, neither. But teaching this as if it's a fact is problematic.
A sensible policy would ensure that the curriculum is agnostic to these beliefs.
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