> Not providing a 10 year old with puberty blockers when you suspect that it is because the child has been manipulated into believing that they have gender dysphoria is practicing medicine. So I am not proposing that we deny anyone access to medicine.
Of course if there were some specific reason to believe that the child was being manipulated, then it would be medically appropriate not to treat them with puberty blockers. But you said "this is a serious hole in the argument for providing gender affirming care to children" as if you think this should be the overriding concern even when there's no specific evidence that the child is being manipulated. That is what I take issue with.
Suppose that we were discussing an influencer parent who was exploiting their child's blindness for social media views. Would you be telling people that it's just as likely as not that the child is just pretending to be blind to satisfy the parent with Munchhausen's? If not, you're special pleading: https://en.wikipedia.org/wiki/Special_pleading.
> Parents with Munchausen's manipulating their prepubescent children into socially transitioning is a good explanation for the rise in prepubscent children socially transitioning
It's a very poor explanation, because more people of all ages are transitioning more than in the past, not just prepubescent children. It also stands against an obvious and much simpler explanation, which is that children today are more likely to encounter the idea that someone can be trans and much less likely to be told to suppress non-normative gendered behavior.
> we must allow ourselves to consider the possibility that it happens a lot, since Munchausen's is at least as common as gender dysphoria.
You say that as if it means that a given child presenting with gender dysphoria is just as likely to have Munchausen's by proxy as actual gender dysphoria. But there are tens of thousands of possible conditions someone with Munchausen's might imitate instead. We should expect that the fraction of them that imitate gender dysphoria is dwarfed by the number of people who actually have gender dysphoria.
It's telling that your argument is entirely theoretical. If there were a significant number of children manipulated into socially transitioning because of Munchausen's by proxy, there would be actual confirmed examples to refer to. If it were a large-scale social problem, there would be data on its prevalence. But there isn't, because this is a scenario fabricated to apply unjustified scrutiny to children with gender dysphoria.