Flannery O'Connor was conscious of being a "Catholic Writer in the Protestant South" (that's the title of one of her essays). "The Displaced Person," like all of O'Connor's stories, is written from a distinctly Catholic viewpoint. One of O'Connor's stated goals of her fiction was to share her religious vision with her readers. This doesn't mean that you have to be religious to appreciate the story or to wonder at her complicated viewpoint. She uses religion to explore a number of compelling issues, including poverty, racism, and immigration.
Mrs. Shortley experiences a religious transformation just before her death.
Father Flynn abuses his authority by forcing his religious beliefs on Mrs. McIntyre when she can't protest or leave.
The Priest is doing his religious duty by preaching to Mrs. McIntyre, whether she likes it or not.