I don’t know if Hermione is strictly a self insert any more than her other characters are, we just sort of assume that because she’s the girl. Oftentimes we see Rowling pop up in the framing devices and not the characters themselves. We are always drawn to some conclusion the plot wants us to. Often what Hermione does is a lampshading technique. She brings up the issues around moral issues but we are lead to see her concerns and advocacy as invalid as the plot makes them inconvenient or proven to be incorrect. It’s the actions speak louder senario. What the characters individually say is not wholly important because from an authorial standpoint some of them are intended to be misguided and Hermione is framed as good-hearted but ultimately misguided.

Hermione’s sense of moral objection is treated more often as a flaw, an annoyance to her peers and unneeded or even counter to the needs of by the people she is advocating for. She is more closely aligned to a caracature of how JKR veiws advocates of minority rights then a reflection of her own advocacy. That every other character tends to just ignore Hermione isn’t veiwed as a tragic instance. It’s played for comedy.