Trans women are an ideal target. Unlike previous victims of this technique (Jews, Black people, Muslims, Gay men, Irish, Romanians, Somalis, take your pick) trans women are so few in number that your chance of actually meeting such a person and having your prejudice challenged by reality is quite low.
Rowling's original concerns were based on the highly unlikely premise of the abusive "man" claiming to be a trans woman to gain entry to female-only refuges. This is a fairly unlikely scenario, but in the way it interacts with the law it is no different to a situation that does arise with women fleeing abusive same-sex relationships. Surprise, surprise, the people who run these spaces are very aware of the risks to the people within, and "I am a woman" has never been grounds enough to be granted access.
I do think the vitriol she was met with from some well-meaning but unhelpful quarters after her first pronouncements had the effect of driving her away from civilised debate and into the orbit of some really nasty specimens, from where she has been given moral support to double down on her uninformed and hurtful pronouncements.