NTA and in fact I think discussion should always be encouraged about any work. We are at a time where teens are growing less and less capable of critical thinking and so it is always great to encourage it, especially within text. HP is an older saga and it reflects not just JKR, but England itself in the 90’s-2000’s. As such, there are things which were fine then but aren’t now, some of which she most definitely will catch on at 13. To give her that wider view of the world and of literature could be really great for her.
BUT in order to encourage critical thinking you need to offer a non biased view of things. That way she won’t follow what you said, but rather what she thinks is right, which may or may not change with time. Plenty of people haven’t dropped Harry Potter or other sources of media with ridiculously awful creators but are still deeply aware of what they are and the in universe issues. JKR is not the first and won’t be the last, and there are other ways to make up for it. In her case, donating to trans charities, spreading awareness and attempting to make fandom and the series more inclusive are some good alternatives to outright dropping the series entirely if people really don’t want to.
That does not seem to be what you’re about to do from what you wrote. It seems you want to tell her to drop it because it makes you uncomfortable over JKR (which is your right to feel). On top of taking away her opportunity to learn and choose, the problem with that is she’s 13, and I haven’t met a single teenager that does something they don’t want to do unless they’re forced to. If you get pushy about it, it might even harm your relationship. So be careful as to how you handle this.
TLDR; NTA for wanting to discuss JKR and in canon. issues with your cousin, might be TA for trying to force her to drop it in case she chooses not to.
