There is no gender controversy, The main pink playable Birdo it's a girl.
It's the people who still confused about it.
Nintendo developed the playable pink female Birdo into a major character in the spin-offs of the series, her name is due to the fact she is a member of the species of the same name, so that's not her name, same goes for Yoshi, who is a male. All Yoshis are shown to lay eggs, though not all are used for reproduction. Most are actually used as weapons.
The male Birdo (Japanese: Catherine) was seen as a boss in super mario bros 2,also he reappeared in the japanese video game: Captain Rainbow.
Although Captain Rainbow also makes reference to Catherine's gender controversy, giving him a distinctly male voice, and by the situations Catherine stumbles into, although in the game Catherine's indeterminate gender also forms the basis for a side-quest to find proof that he is a girl So, Catherine certainly exist.As you said, Birdo is a member of the species of the same name, so we have two notable Birdos. The cute and funny female Birdo (partner of yoshi) ; And a really confused birdo who thinks he is a girl.
Everyone loves Birdo as a girl, so please people of Japan/America if you can see this , please, stop refer to Birdo as a male, Birdo is a girl and she makes a cute couple with Yoshi n_n