It seems only intuitive that if I get to define my own gender identity, as I have and as the world lets me, then everybody else should get that same privilege. And yes, I would say that denying that privilege from some people while granting it to others is inherently hateful.
You can swing your fist all you like, but you can't punch me in the face and claim that I'm infringing on your right to swing freely. You can have all the personal beliefs you like, but as soon as you start imposing them on somebody else's identity, they're not personal beliefs anymore and you don't get to enforce them on other people. When you misgender somebody else, you're imposing your own personal beliefs on them, and that's wrong.