Biological sex is fixed, and in almost all cases gender is aligned with biological sex. Trans people can identify as a gender but it doesn't change the fact they're biologically not the gender they feel they should be. There's really nothing that controversial in these thoughts, it's not hateful, it's not disgusting or demonising as some seem to think.
One thing Rowling (as far as I've seen) doesn't seem to think is gender being different to biological sex?
Try starting from the opposite question - when does biological sex actually matter? It might matter in some medical situations - along with other aspects of someone's medical history. It might matter in some interpersonal relationships. But most of the time it only matters to the individual, and if that's the case it's the individual you need to talk to, and that's the part you need to respect. Whether that's a he/she pronoun or the choice of a hairstyle or which bathroom they go in.
The trouble comes when people like Rowling suggest that you can't respect individuals, except at the expense of biological women (though that term in itself is fuzzy, with intersex and DSD women a non-trivial minority).
Rowling says she approaches it from the position of being an abused woman herself - emphasising a theoretical hazard created by a "male-bodied" individual in a setting like a women's refuge or a prison. A reasonable question, but equally reasonable if the question was posed about a strong, violent, predatory biological woman. Into everyday life, women's spaces (like public toilets/changing rooms etc) don't suddenly become more dangerous because the law says they're about gender, not birth sex - predators always knew how/when/where to hide.
There are complexities. The shared bedroom in a women's refuge (or cell in a prison) where psychological stress/fear of a "male body" by another woman needs to be respected. But that's an argument about funding and organisation, not about amplification fear of a minority of a minority into some kind of broader fear. At a more trivial (but still important) level - as I've said previously on here, I think women's sport at the elite level needs to be handled carefully if it's to maintain both credibility and fair competition.
Rowling seems to take those issues that test the principles hardest, the outliers if you like, and places them centre stage as if there's some kind of broader, novel threat to women being created by a movement that's about respecting individual as individuals. It's disingenuous. Exaggeration to make a point? Maybe, but then if you want to exaggerate, you can expect exaggerated reactions in response.
you accidentally posted a good, considered video that made a decent case against J.K. Rowling, thinking it was that awful video of awful Blaire White. Not all trans YouTubers are created equal.