This is a great question here. As a cis person who grew up being taught that being trans is "unnatural" and treatment for it were essentially mutilation, the only way those ideas melted away were when I met actual trans people. When I met actual trans people, who were just normal regular people, and their transition felt natural and normal in practice, I was astonished at how normal and natural all of this was. My whole life I had been taught that all of this was wrong, but when I saw it in person, it wasn't. Knowing actual trans people, who weren't doing anything wrong, but just wanted relief from dysphoria, normalized everything to me. I often hear about trans parents who were most of their lives vehemently anti-trans, but then when they saw their kids suffering, at some point realized their child needed something that went against their beliefs, and like many good parents, put their child's need first, which forced them to change their ideology. Knowing an actual trans child, instead of just a theoretical boogey man, humanizing these children, is the key. It's easy to disagree with trans people as a concept, just like it's easy to say no to something that's wrong. But when you're there, actually talking and looking at an actual, innocent child, and this is what they need, changes the stakes. Who are we to make medical decisions for people we don't even know? Let's leave it to their doctors.
It's easy to hate a concept, it's harder to hate a person, it's even harder to hate a child.