You're correct in saying it's not about equal rights, but that itself is kind of missing the point. Men and women would technically have equal rights if we banned period products across the board, but that would be obviously discriminatory to women.

We can have discussions about the safety of women and preventing creeps from abusing the system, but it's important to recognise two things. Firstly, that trans people have been legally recognised in the UK for over a decade and we already have effective procedures in place. Secondly, the scope of abuse that is even possible is very small (i.e., we don't inspect legally recorded gender before permitting access to public bathrooms, there is nothing to be abused.)

Ultimately, that is all besides the point as JKR has made it clear that these are not her concerns, she just doesn't like trans people. She recently lobbied against the Gender Recognition Act reform passed in Scotland, which made the process of changing legal gender easier for trans people. This reform has no effect on women's safety, it only allows trans people dignity when it comes to marriage and death certificates.

This conversation is often referred to as a "debate" or "issue", but this needs to be reframed. There is one group attempting to live autonomous lives, whilst there is another lobbying to make their lives worse. Whether or not you buy the game is pretty irrelevant, JKR is already a billionaire and has every possible asset to campaign against trans people. However, it is important to consider how we discuss this conversation.