The loathing of trans people (trans Women in particular) by a lot of rad fems emanates from a position of misandry, in Rowling's case this most likely grew out of her abusive relationship with her ex husband who is completely detestable. This then becomes the very thing they claim to be victims of, misogyny, when they attack trans Women (for not being effeminate enough, for being too effeminate, for being just a "man in a dress")...
The problem with Twitter is that opinions are already formed, people are on there to convince others, not have their own opinions changed. The ferocity and arguments used get more extreme on both sides in an effort to disprove the other person. Until the point whereby their original arguments are defunct and it's a concoction of extreme views and falsification - on both sides. As Friedrich Nietzsche said - 'He who fights with monsters might take care lest he thereby become a monster.' Twitter is the abyss and these people spend all of their lives hitting refresh for the next battle.
Rowling has rather intelligently used this to spearhead her reputation as a writer, the rather ludicrous fallout over the character of a man who wore a dress to murder victims was the accumulation of an extremely calculated plan. The right people fell for it.
However, Rowling has now shown her full hand - Robert Galbraith, her rather unfortunate pseudonym, is steeped in historical anti gay sentiment. One of the real Robert Galbraith's was a pioneer of gay conversion therapy claiming to have successfully converted a homosexual man to heterosexuality using electroshock therapy to the brain.
Promotion of an online store which is steeped in misandry, with anti male bric-a-brac ("Dead Men Don't Rape!?") and transphobic paraphernalia has shown just how extreme her views have become.
However, people may and still do argue that her views aren't extreme, that Mermaids are wrong and that there hasn't been any damage whatsoever. It could be said, that her antics have proved to be diversionary. Hidden behind the Cold Twitter War something more sinister has happened, the reformation of the Gender Recognition Act was announced in England and Wales. Whilst everyone's attention was turned towards a character in a dress and the author's merciless barrage; behind the scenes the real issue of trans rights were being settled and the results were shocking - they slapped a discount on the process, keeping all that is wrong with it intact.
Let's be clear, like in Hungary the reversal of trans rights didn't just affect trans people. There are now LGBT free areas. Women's rights have taken massive steps backwards. The attacks on trans people aren't just a concerted effort to demean and eradicate trans people's legal rights, trans people are just the easier target. They're not just coming for my rights, they'll be knocking on your doors as Men, Fathers, Husbands and Homosexuals. They are the personification of a Karen.