I think I read this in a Gardner Dozois Anthology of Best Short Science Fiction Year X. The year would have been 2005 or earlier. The story was about a boy and a girl, about 13 years old initially. They lived in a world that was essentially the same as here, as our Earth. Reproduction was quite different though, and that is the beginning of what I don't understand.
Men and women can't reproduce without the assistance of an "uncle" as this third sex is called. Adult men and adult women look like adult men and women in our world. The third sex is an overweight, sexually ambiguous person who the boy, the protagonist, describes as smelling yeasty. He occasionally sees his family's 'uncle' or de facto sex facilitator, visit the family. One time he catches a glimpse of his parents during a visit. The father is standing behind the uncle and the mother is in front. It isn't just his family who is like this. Everyone's is.
At puberty, it is determined whether one becomes male, female, or an uncle. I don't know if this happens naturally, or if it is facilitated in some unspecified way that I didn't pick up on. The boy and the girl are good friends and talk a lot. As they transition through what seems like human puberty, they kiss, and are sexually intimate. They are worried about anyone finding out that they're having sex, but not because they are too young, or fearful of getting pregnant. Rather, sex is not supposed to be like that, and should only be with uncles.
The normal age when children go through the process of puberty that determines which of the three genders they will be is at about 14. The boy still hasn't had this happen yet by the time he is 16. The girl is a year younger, at 15. They are puzzled why the boy hasn't gone through whatever this mysterious gender transition is yet. One day after they have sex as usual in their hideaway, something happens, and the boy wakes up in the hospital. The girl visits him, and tells him that he nearly died. Surgical intervention was necessary for him to go through puberty. He can no longer have sex like he did before, and by the end of the story, the girl has become an 'uncle'.
The story has a 1950s era feel to it, of family life and suburbia, and is tinged with melancholy.
What is the name of this short story?