A&P is narrated by Sammy, a 19-year-old cashier at the A&P. Like many first-person narrators, Sammy seems to be telling us the truth as he sees it, but he's unreliable because his point of view is limited. Like many teenage narrators (think Holden Caulfield of The Catcher in the Rye), he sees most adults as "sheep" or followers, all indistinguishable from one another. The people in this story are not meant to represent fully fleshed out human beings, but rather to symbolize the spirit of conformity Updike saw among many Americans in the early 1960s.
While Sammy's limited perspective might make him unreliable, it also paves the way for some pretty major growth on his part. It also shows us that he's willing to think and act differently than the people around him.
We think the fact that Sammy's point of view changes over the course of the story is more important than his reliability as a narrator. At the beginning of the story he's simply whining and complaining (in his mind) about the conformity, uniformity, and dullness of his community. Queenie and the other two girls show him a simple way of mocking this conformity. By wearing their bathing suits into the store, they mix things up a little. Sammy follows suit by removing his A&P bow tie and apron when he quits, expressing solidarity with the girls and using his clothing, like them, as a form of activism. Over the course of the story, he goes from complaining about what he sees as a problem to actually doing something about it. That's a lot of growth in just a few pages.