Ramen no Oujisama has that feature. Just use the genderbenderxyz secret code to enable the choice when you start a new game. Infinite Desires by default assumes a dude as a protagonist, though since the setting of the story is in an alternate earth in a multidimensional futuristic world, turning the dude into a girl or something else for different situations isn't out of the question down the road. :).
Viewing post in Infinite Desires v1.1.3 / Godhood Poll! comments
Hello. Earlier reply already explains the situation about Godhood. To repeat, It's a technical problem I can't help fix simply because I don't know about the engine that powers the game. I know you're a real a fan of the game, that's real cool and we appreciate that, but Godhood development is on pause/hiatus because of this. Thank you for understanding! ^^V