In order to understand the part religion plays in the story, you must first understand a little about the author. Flannery O'Conner was a devout Roman Catholic and considered the idea of "grace" as a "divine pardon from God" that is freely available from God just by asking for it. Faith is undeserved and comes at a moment of great insight. In the story, the Grandmother, who is a decidedly unlikeable character, obtains grace at her death. As she is dying from three gunshots in the chest fired by the Mifit, she reaches out to him and sees him as one of her own children. The Misfit replies that "she would of been a good woman ... if it had been somebody there to shoot her every minute of her life."
To O'Connor, this recognition is an indication of grace. Ironically, one of the least deserving and most disliked character in the story is the one who achieves grace. For O'Connor, this means that grace is available for everyone, even those who seem the least deserving of it.