@BonfireLady , you're right when you say, "The belief isn't the issue."
What does seem to be the issue is more the seeing of belief in gender identity as what it is: a belief in just the same way (and with the same status) as other beliefs such as belief in ghosts, gods, angels, paranormal auras, the healing powers of crystals, and so on.
We don't allow believers in angels or auras special access to children in our schools (although we do allow such believers to set up their own schools, given reasonable safeguards). Nor do we allow such beliefs to influence our laws or our wider society (although, again, we don't stand in the way of such believers getting together to express their beliefs to one another and so on). We don't sneer at people who believe things we don't (at least in public). We treat people politely, however daft we may think them.
People believe all sorts of different things. We rub along. You want to believe you have a guardian angel? Fine. You want to believe you have a gender identity? Fine, again. Just don't expect the rest of us to behave in line with your beliefs ... and don't expect our schools to teach your beliefs as though they are fact, or our laws to be based on your beliefs.
We escaped societally-mandated religion some time ago. We should not allow our society now to mandate this new gender-identity belief.
"Nice but misguided" people? Smile, OP, and accept them as they are. Keep the kid gloves on. But if they start to support the imposition of beliefs such as in god or gender identity or whatever on us or our children, we need to take the gloves off, as appropriate.