The problem with that statement is there's not a very concrete definition of hate speech and that's a humongous problem with woke culture today.
I'm democrat, I support rights for all these people, but there's a lot of nuance in what people believe or say. If it's convenient to you to group people as instruments of hate, you can do that, but that's not an accurate view of the world and I don't believe it does any good.
Of course there are lines, but Rowling clearly falls under meaningful policy discussion. She's calling on not to hate and doxx scientists and for more discussion and inquiry to be had about people's right to transition genders before the age of 18. She fully supports a trans persons' right to live as they please.
If you fully believe that science supports the existence of trans people, then support science too. Do you believe this way about global warming?
If someone proposes a policy idea you don't like, you can publicly disagree with them all you want and if it's a flimsy policy it will fall apart. If you're launching campaigns labelling them as guilty of hate speech, you essentially want to shut them out of the public sphere and that's not something I would get behind in a million years. On that alone, I would support JK Rowling's contribution to the public discussion of trans people before I would protect the right of trans people to be shielded from words entering the public sphere that they don't like.