The thing is, they don’t believe in gender dysphoria or a healthy way of being trans. In their (wrong) world view, a minor transitioning is being sexually abused by their parents for a fetish or a political belief. They believe they are protecting these kids from being mutilated and mentally groomed into being sex deviants by abusive parents who want to ban their kids being straight or cis for political brownie points. They think that being trans is a cross-dressing and humiliation fetish forced upon children due to the parents’ ideology.
Of course that point of view is utterly wrong, but it’s hard to argue privacy with them if, in their world view, it’s kids being mutilated and scarred for life.
This is simply to say that if the base assumptions are different, these arguments can lead nowhere. If their world view was correct (it isn’t), it would be entirely reasonable to ban such a cruel grooming and sexual abuse practice, and it would probably also justify all the hate and vitriol - we would probably do the same if the base assumption was correct, and it would be infuriating if the other side would excuse it with “none of your business I am abusing these children”.
The only difference is that their world view is ostensibly not correct, and being trans is not what they have been convinced it is.