That's not "gender re-assignment surgery". Do you make any distinction between hormone blocking drugs (puberty blockers) and hormones?
Sure, I don't think that doctor's should treat children like laboratory experiments even if the children are requesting to be treated that way.
I think we understand "support" very differently.
I believe that there can be well intentioned supportive people that can still be a bad influence. It is why I encourage christians to be the supportive person in the life of a transgender individual they know and relate to.
If the person is seeking out that comfort with activists and some other members of the trans community, it is my opinion they are more likely to mutilate themselves than if they have the support of friends and family with good morals.
I would say if you have a child or sister that is transgender than you need to show them love and let them know that they are loved and worthy of love and give them positive reinforcement if they start having a negative self image. If they say "I hate myself" the relative in their life should say, "you are inherently worthy of love and you will always have mine"
If a person struggling with gender identity issues doesn't get that love from the people close to them, they'll get it from people in other communities.
It's the same reason kids turn to gangs. They are getting support from the gang . The gang is supportive of them. The support I believe generally is well intentioned, it just leads to bad results.
Same thing with incels. People hate them and then they find a group of people online that do support and understand them, and the spiral begins. You'll see the same supportive movements in fat acceptance that lead to an attitude of being happy, being unhealthy and encouraging unhealthy habits. The being happy with themselves is good, their community is supportive and they will die at 40 anyway because they couldn't get the support of fitness motivated people in their own lives.