what if he's not NT?
Probably even more important that he has multiple support networks. He's growing up and you wont be able to do it all for him forever.
If he's been given a card for a dodgy organsation then by all means raise hell with the school but otherwise I'm not sure what wrong advice the nurse could have given.
I just can't help feeling this is deflection
It might be a deflection from the issues that you judge are most important for him but he's old enough to have his own priorities and follow his own path. Which might end up at the same place where you started, but he's too old for you to decide for him what his priorities should be. So for example if he thinks he's trans then that's where he is and his ASC is just another part of the mix and for him, and not necessarily the most important part.
I would do whatever I could to talk up that you can't change sex, that gender stereotypes are rubbish, that Boy George had long hair and wore makeup etc.
Try to avoid asserting your own views. Listen, don't talk. If this is a gender thing then ask him what he thinks gender means, what sex means, etc., what he wants to do. There is no need to have all the answers or even any answers, let him tell you. And he wont care about Boy George, that was before he was born.
I have talked and do talk to my own DS about such things as he has an ASC and has a close friend who was is/was trans-ish. His friend was satisfied with watchful waiting and some cross dressing. The single most powerful thing I could do was to get DS to tell me what he thought.