By not exposing them to the idea in the first place. If it is a mental illness and/or a mental contagion, then there is no sense in confusing and terrifying otherwise healthy children about it. Like with 'demons' and other medieval hysterias, the solution is not to speak these things into existence in the first place but to come to a true understanding of the underlying malady and then apply solutions to those who are afflicted when encountered.
But this is a separate issue, the issue of stigma, which is not the fault of the afflicted at all but actually an issue of those projecting their judgement.. and that is something to be tackled separately, through better understanding and awareness (in the judging party). We should not seek to treat the symptom, protecting the judged, but treat the cause (the judging party).
It's not about hiding or forcing. We are all in this together. If it is a mental illness and/or contagion, then it is our duty to get to the bottom of the truth about it so we can then help those who are afflicted. Not out of a sense of puritanical moral imperative, but just as human beings wanting others to be healthy and happy. But the underlying point is, the truth is the truth, regardless of how uncomfortable it may make us (or an afflicted person) feel, and we have to face it from that direction.
I keep saying I don't hate these people, perhaps I should also state I despise the attitude of the 'puritanical moral imperative' that seems to pervade many who ride on the criticisms of transgenderism (or homosexuality, etc). I'm interested in the truth, and in true well-being for the individual. If people choose to want to remain in their afflicted state as it were, that is their choice.. people have a right to refuse treatment.. but what I fundamentally do not agree with is those within that community who wish to forcibly push their state on to otherwise healthy people, especially children.
Like overweight people as you mention, or suicide rates amongst children, these are all ultimately symptoms of a sick culture itself. We owe it to each other to try and figure this all out, otherwise what the hell are we doing as humans anyway?