The nuns are yet another example of a minor character (or in this case, a set of minor characters) that exist only to tell us about Holden. We don't know enough about the nuns to analyze them as characters, but we can delve into the way Holden views them and, consequently, what that tells us about Holden.
Take his conversation with them about literature. Holden has claimed before that he's not too smart. His brothers and sister, he says, are about fifty times more intelligent than he is. But the Romeo and Juliet conversation reminds us that, while Holden does have issues with formal education, he's a smart guy. His thoughts about the play are far from trivial, and he delves into the emotional gut of the story to identify what is indeed one of the most tragic moments of the play: when Mercutio dies. The point is, Holden is both intellectually and emotionally sharp. He knows what's up.
And not just in 17th-century literature, either. Holden's observation that nuns "never [go] anywhere swanky for lunch" is perceptive and touching (16.1). Like his interaction with Sunny, this shows us how compassionate Holden really is. He constantly puts himself in other people's shoes, has a sharp awareness of those around him, and thinks conscientiously about how that relates to his own position in life—like how it bums him out to eat eggs and bacon when the nuns are only eating toast and coffee (15.18).
And that leads us into a digression about money and religion: if one person has money and another person doesn't, it makes it hard to spend time together. He concludes the same about people from different religions; Catholics are always trying to find out if you're a Catholic too, he says, because they'd enjoy the conversation more if you were. In Holden's mind, all these constructions create social barriers. For an isolated teenager trying to make a connection with someone, barriers are not a good thing.