This can be disproven pretty quickly, and has been in the last couple of pages of the thread. There are loads of examples of Rowling's politics coming through in Harry Potter, often by her own admission.
The argument of "they're kids books, they're about wizards and elves, who cares" falls down because most of them are aimed at YA audiences and Rowling self-admittedly has a crack at making points about things like racism, fascism, slavery, discrimination, politics, corruption in the media etc. It's certainly nothing new for people to be interested in the viewpoints espoused in the books young people read, and it's nothing new that people engage critically with the themes of popular and influential pieces of media (particularly ones which were ubiquitous during their own childhoods). That goes double for instances where the creator of that media goes on to become a significant political activist in their own right. I think a mistake you keep making is that you're attributing the familiarity of some of her critics with the minutiae of Harry Potter to obsessive nitpicking born out of hatred, when in reality the reason her critics know so much about Harry Potter is that they're largely people in their 20s and 30s who grew up on it and are (or were) fans when they were kids.
Rowling's issue is that she wanted it both ways with Harry Potter. She wanted credit for addressing political and social issues in the books but didn't want the scrutiny that comes with that. She can't seem to grasp that if you include moral themes in your writing, you can't decide which bits of your books are meant to be a moral lesson and which aren't.
For example, she was rightly praised for setting up lycanthropy in the Harry Potter world to be an analogy for HIV and highlighting the societal stigma of being HIV-positive in a way that was relatable to younger audiences. But if you're going to build up that analogy and talk about it in interviews, you have to accept that people are going to be a bit confused if you later introduce a werewolf antagonist whose MO is, basically, going around intentionally giving HIV to children (which is almost a perfect combination of two classic homophobic tropes - spreading disease and preying on children).
Now, I personally think a lot of this stuff (including that example) comes from a combination of her limitations as a writer/"thinker", ignorance of the issues she's trying to address and a big dollop of arrogance, rather than it being an example of outright bigotry. There is a bunch of stuff though which absolutely reflects some pretty ugly/weird/regressive attitudes, and her habit of getting hyperdefensive when called out on anything (going back to way before twitter), never mind how minor, makes it's difficult to parse out the two. And then of course, people who have seen her going off it about trans people on twitter are less willing to give her the benefit of the doubt on stuff that they might have done beforehand.
Edit: also, providing Twilight and Percy Jackson as examples of works that aren't scrutinised for their themes is funny, because Twilight sparked a massive debate online about the unhealthy relationship dynamic it was romanticising, and Percy Jackson is often praised for it's portrayal of neurodivergent characters. Obviously it probably doesn't cross into 'real news' like the Rowling stuff because neither series is as famous or popular as Harry Potter, and the authors of those works haven't leveraged their fame to push controversial beliefs in the way Rowling has (despite Meyer holding quite a few)!