Id still call them a gingerbread man. It's not really something that needs changing is it? Couldn't people who have a problem with it just think of the man bit as meaning mankind
I'm not too sure. After all this is a gingerbread pussy, but try Googling "gingerbread pussy" and you'll get something quite different. The name of the cookie an carry a lot of weight!
I think we're all aware that it's a biscuit. and the price is for one, so the tense is correct (person, not people) But it's the shape that gives it the name, at least it used to.