The typical Monty Hall formulation has similar ambiguity because it’s not clear whether or not the host knows the right door. Just like in this question, it’s not clear if the “narrator” knows the first child is a girl.

(Also, this problem has an additional layer of ambiguity where “birth order is irrelevant,” but MF and FM are treated as distinct items in the probability set. Is the order irrelevant to the probability, or is it impossible to distinguish the age of the two children? It would be clearer to simply say “each birth is an independent event.” One of the comments on the blog explains this better than I can.)