> Parents with Munchausen's manipulating their prepubescent children into socially transitioning is a good explanation for the rise in prepubscent children socially transitioning. If we allow ourselves to believe that this scenario exists, then 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 seem to have confused what used to be called Munchausen's syndrome and Munchausen's syndrome by proxy. Or where you got your information did. Now they are called factitious disorder imposed on self and factitious disorder imposed on another. Factitious disorder imposed on self is estimated about as common as gender dysphoria. The ranges overlap. Estimates for factitious disorder imposed on another are much lower.[1] And most cases involve infants or very young children. Probably because older children can speak for themselves and are less pliable.

[1] https://my.clevelandclinic.org/health/diseases/9834-factitio...