Baba is not a particularly religious person, and in fact, he seems to be against the kind of religion that gets taught in school. When Amir comes home and tells him what he has been taught about sin, specifically that Islam considers smoking and drinking sinful, Baba dismisses that version of religion. Instead, Baba has his own kind of theology. He tells Amir,
"Now, no matter what the mullah teaches, there is only one sin, only one. And that is theft. Every other sin is a variation of theft. . . . When you kill a man, you steal a life," Baba said. "You steal his wife's right to a husband, rob his children of a father. When you tell a lie, you steal someone's right to the truth. When you cheat, you steal the right to fairness. Do you see?"
This definition of sin as "theft" and of all other sins being "a variation of theft" later becomes ironic, as Amir learns that Baba was also Hassan's father, and he never told his sons the truth. Amir feels that his father stole the truth and all of the subsequent effects of that truth from him. He even believes Baba's lie contributes to Hassan's death, as Amir feels if he knew Hassan were his brother, he would've acted differently toward him, and maybe Hassan and Ali would have gone to America with Baba and Amir.
Baba and Amir are Sunni Muslims, and this is the majority religion in Kabul. On the other hand, Hassan and Ali, their servants, are Shi'a Muslims, and because of that and their ethnic group, they are persecuted in Afghanistan. Baba's majority faith probably allows him to be more blasé toward religion. It's also possible that losing Amir's mother during childbirth led to a crisis of faith for Baba.