Why is "The backlash against JK Rowling" "woman-hate"? Because JK Rowling is a woman?
I had a long discussion about JKR's tweets and the criticism with my two LGBTQI children, both have been fans of JKR's fiction and both felt her tweets were cis-centric if not trans-phobic and anti-queer. They are feminists, in the sense of equality for all.
And I don't know what you mean by "backlash". IN Susan Faludi's original use of the word it meant the reactionary conservative response of the powerful at the slightest threat to their power. Is JK Rowling making fewer millions?