Although everyone in the community is the same, and sameness is a high priority, the people are not EXACTLY the same.  There are no identical twins.  If a set of identifical twins is born, they are weighed and whichever twin weighs less is released.  We first learn about the release of identical twins in chapter 14, when Jonas's father says he has to release one of a set of twin boys once they are born.

When Jonas requests to view the release in chapter 19, he comments on why there can't be identical twins.  The Giver says he wishes they would not release one, and Jonas replies:

"Well, they can't have two identical people around!  Think how confusing it would be!" Jonas chuckled.

Confusion and discomfort are to be avoided at all costs.  Lily’s story in chapter 14 is an example of the community’s reaction to identical twins.