Maybe I am explaining poorly. When I say that they want them to "not exist" I don't necessarily mean that they will literally be killed (although I do worry that it might eventually come to that). I mean that they will be forced out of social visibility and effectively memory holed. To give some examples:
The right is passing laws saying that you can't teach about trans people or gender in schools. Part of the job of schools is to teach kids about the various important social/cultural/ideologies that make up the world; things like history, capitalism, communism, democracy, dictatorships, the various world religions, atheism, etc. Forbidding teaching of a major element of society like transgender people is in effect an attempt to erase them from social consciousness.
The right is passing laws anti-drag laws that define obscenity so broadly that it can be used as a threat to suppress drag performance. Attacking a culture's artistic movements is a classic way to attempt to suppress it from the public sphere.
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.
The right is passing laws saying that you can't teach about trans people or gender in schools. Part of the job of schools is to teach kids about the various important social/cultural/ideologies that make up the world; things like history, capitalism, communism, democracy, dictatorships, the various world religions, atheism, etc. Forbidding teaching of a major element of society like transgender people is in effect an attempt to erase them from social consciousness.
The right is passing laws anti-drag laws that define obscenity so broadly that it can be used as a threat to suppress drag performance. Attacking a culture's artistic movements is a classic way to attempt to suppress it from the public sphere.