Cheat Code Central has a short article about gender in South Park: The Stick of Truth.
More information.We've come to expect certain things from our RPGs, and the ability to save anywhere is a big one. So is some element of choice, even when it doesn't have a major effect on the story. However, the biggest is the ability to decide our avatar's gender during a character creation progress. If we're able to decide everything else about our character, it only stands to reason that we could choose whether it is a he or a she.
Which is why it would initially seem odd that South Park: The Stick of Truth, a game that gives us so much control over our character's appearance, would make every player male. However, while it may seem like an issue and something we should question, it really isn't. In fact, the gender of the New Kid doesn't matter at all.
For the sake of the story, yes. The New Kid is male. Trey Parker and Matt Stone had a story in mind, and the gender had to be set for certain elements to work. Without getting into specifics, one of the storyline quests on the third day involves pretending to be some girl's boyfriend. Despite that moment, and a few similar ones, players aren't really forced to think of the New Kid as being male or female.