This is an interesting point.
So, this actually isn't the first time she's attracted criticism for her political views. I remember in the run up to the Scottish independence referendum a lot of Scottish nationalists criticised her for sticking her oar in, and particularly for being an English woman who had chosen to live in Scotland and was publicly opposing Scottish independence.
I don't remember how much criticism she got for her pro Labour and anti Brexit stances, possibly not that much because her fan base was naturally more left leaning and pro Europe anyway.
What I think is really noticeable about the criticism she has had from US-based liberals about her stance on women's rights is that they've all accused her of being right wing. To me this shows that these people who no doubt like to think of themselves as the intelligent Americans were completely unaware of her previous political activism in relation to subjects they have no interest in because they don't affect America.
When I first heard internet rumours about JK Rowling being an evil bigot who had been brainwashed by the far right into hating a vulnerable minority, my gut reaction was, "That sounds incredibly unlikely."
If you're aware of her other political positions, you understand that being in league with the far right just doesn't fit. If you're not aware of her other political position, you're more likely to believe that rubbish.
Perhaps this is a stupid analogy, but imagine that in the US, Trump supporters suddenly started putting the "u" into words like "colour". And then JK Rowling tweeted something with the word "colour" in it. Only someone who was completely unaware that everyone spells it "colour" in the UK would interpret that to mean that JK Rowling is a Trump supporter. It is a position that necessarily requires a certain level of ignorance about the politics of other countries.
I think it is this US-centricism which annoys me the most in all this. You invent a stupid ideology which is harmful to women and children and you either don't realise or don't care because your country treats women and children appallingly anyway. The people who oppose your stupid ideology in your own country are on the political right. Then you export your stupid ideology to the rest of the developed world, starting with other English speaking countries. Then a famous British woman who cares passionately about women and children speaks up about your stupid ideology and the harm it is doing to women and children. And because you're a complete ignoramus who doesn't take an interest in anything that happens outside your own borders and you don't know that this woman is a dyed in the wool leftie, you reach the conclusion that she is in league with the political right in your country. (Even though the political right in her country is still to the left of the political left in your country.) Of course it does not even occur to you to consider whether she might have a point about the women and the children.