@Maniak many religious people claim to feel the presence of God and angels as support of why they believe in such concepts. As an atheist (and even when I was a Jehovah's witness) I have never felt such things. If that's what people want to believe in, that's fine.
However, if they started insisting that I and the rest of society have to change our definitions and laws and language, we have to give up or lose certain rights and protections that are in place for vulnerable members of society, that schools and universities have to teach these concepts as the truth, than any resistance or criticism to these concepts mean you are a heretic and should lose your job or livelihood, you have to alter your sexual orientation to accommodate such beliefs etc etc, then I have a big problem.
Those who have responded here have already said things like if they woke up in a man's body, they would still feel like a woman which implies that at least to them, gender identity is a spiritual notion of a soul that exists independently of the mind/body, physiology, biology and so on. It's something else. An essence that cannot be defined but only felt or experienced.
I'm quite happy to class such beliefs alongside every other spiritual and pseudoscience woo. I don't need to develop a belief in God or soul to understand the importance of not allowing some belief systems priority over others or over material reality.