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I’m not actively following the saga, but that seems like a gross mischaracterisation in all directions. I haven’t seen anyone seriously call her a Nazi¹ and her comments aren’t harmless either.
¹ Though I wouldn’t be surprised if it has happened. But then again that’s not saying much on the internet. Doing a cursory search, I found a post² on her own website where she complains someone said she has “uphold [Nazi] ideology around gender”. “Nazi” is between brackets, presumably meaning it’s a substitute for another word, and even then that’s not calling her one.
² https://www.jkrowling.com/opinions/statement-from-j-k-rowlin...
Thats.... not right? She's becoming more and more anti-trans every day. Harmless is a mischaracterization of her stances.