I think Birdo's a girl, because she spits and lays eggs and wears a bow. Everyone knows only female birds make eggs. Also, the booklet that refers to Birdo as a "he" could have some loss in translation. In English, we don't really have any gender-neutral words, but I know that in Spanish, "su" can mean "his/her/your". Maybe there is a word in Japanese similar to this Spanish word that is sort of gender-neutral, and it was translated wrong.