The author makes many references to belief in The Kite Runner. In every instance, the specific religion is not important; what is important is the character's ability to stand up for his/her beliefs. Amir in particular struggles with this. He knows what he believes is right, but he doesn't act.
This occurs many times throughout the book:
Most notably, Amir doesn't stand up for Hassan when Hassan is raped by Assef.
Amir frames Hassan for theft by planting his money and watch in Hassan's hut.
Amir keeps Hassan's rape a secret from everyone, including his wife.
There are many other examples, but these are the most important.
Baba may suffer from the same problem as Amir. However, we never know what Baba thinks, only how he acts, so it is impossible to be sure. Baba tells Amir that the only sin is theft, and he explains how every other sin is a variation of theft. As a boy, Amir sees many examples of how Baba always stands up for what is right and often feels he is inferior for being weaker than Baba. However, Amir later discovers that Baba is guilty of this very sin because he fathered Hassan and lied about it.
Amir regains his self-respect and is able to let go of the ghosts of his past when he fights Assef to save Sohrab. He knows he will lose the fight, but he goes in anyway and faces his fear. For the first time, he is able to stand up for his beliefs. He finds that this allows him to let go of the mistakes of his past.