[Magic.]

I don't think they should be allowed to. I studied Psychology A level and we were told about a young boy whose genitals were mutilated by a dog ... his parents chose to ask doctors to make him "a girl" and raised him as a girl and his twin brother as a boy. Anyway as he grew up no matter what they did he insisted that he was a boy, and ended up having a sex change back to being male.
Basically I think that if the sex of a child is questioned at a young age, for whatever reason, that child should be allowed to get their own gender identity rather than their parents deciding for them. Gender is not just determined by sexual organs, so changing them will not define the child as a boy or girl, only he or she can do so.