She’s not “conservative” she’s neoliberal. Aka she’s for a strict adherence to the status quo while paying lip service to progressive ideas. People in her books can be bad, not institutions. It’s why harry spent the entire last half of the series at odds with pretty much every institution in the magical world and still ends up a magic cop defending those institutions. It’s why slavery is good actually! Because the slaves like it! It’s why they continue to separate the kids by house at hogwarts even after demonizing one house specifically as the fascist house that helps the magic nazis.
The YouTuber Shaun has a very good video on this topic: Harry Potter