The teens I talked to are frustrating on this issue. They say things like "I can't believe someone that transphobic could even have written books about finding and being your true self, it just seems impossible" - and then they don't make the leap to thinking that yes, it does seem impossible, so maybe she's not transphobic. They just keep on with the idea of how disappointed they are that in reality she must be this big transphobe. It doesn't matter if they read her essay either. In their eyes, she is saying that transwomen are not women, and in the teens' eyes, of course they are - that is their true essence, they know what they are underneath, how can we possibly judge them from the outside and decide if they're men or women, sex is much more complicated that simply your genitals or chromosomes or hormones, so they must have some inner feeling that tells them they're women and we are so bigoted for not recognising it. Therefore JKR is transphobic for not recognising that and for denying that they are women. Their biology doesn't matter, they just ARE women inside and it's nobody else's decision. You have to recognise it for yourself and find your true self, and that's the important bit. The characters in her book go on about being their authentic selves and being true, and there she is in reality denying people's true selves. So she is a transphobe, end of story.
It is frustrating as anything because you can't break into this narrative, as it's not based on logic, but on this 'inner feeling'. They are utterly convinced of it, and getting them to read her essay doesn't help (although many of them won't do that either, of course, and prefer to trust the social media groups that tell them that she's transphobic - the obsesed fanfic groups etc are very big on it), because her essay denies the 'inner essence' idea, which just comes down to 'they know they're women and we must support that'. If you try to mention that you can't define that without stereotypes or circular definitions, you get told that you just don't understand.
Maybe some of them do believe in stereotypes, actually, and that is the root of the problem? So boys or girls who don't fit the stereotypes just know they are the opposite sex, and it's apparently cruel of us to deny that and try to make them be something they're not. That must be the reasoning.