// ... for the past year or so I've been in conversation with two young teenagers who assured me that 'Loads' of people in their school who identify as the opposite sex were very genuine and that they were actively supported both by the school and by the other children. ... Now they tell me that the vast majority of them are attention seekers.... This stuff is being force fed to our children - and that has to stop. It's not fair to any of them - including those who really do have a genuine problem. //
I lightly edited the comment above, but I hope you'll agree that it doesn't change the substance.
In any case, I think the revealing part of this is the final word: "problem". Why should transgender people be seen as having a "problem", any more than gay, or bi, people? It's that attitude that, I think, is causing the issue, far more than overenthusiastic support.
What's going on at schools could as well be categorised as a normal experimentation that many children grow up through. Harm is caused when you respond to that experimentation dismissively, or use rhetoric that implies that it's shameful. Inasmuch as we should be careful not to push experimentation "too far", to the point that a given child regrets it, then, sure, we should be careful, but I don't agree at all that this is what's happening, and to the extent that you see this it's because your starting point is so dismissive in the first place. "Attention seekers", "force fed", "a genuine problem"... this is the language that makes it taboo. And, perhaps a touch ironically, the more taboo something is made to seem, the more attractive it can become.
If you do wish to support genuine transgender people, a good way to start is to reframe your language to strip the negativity surrounding it.