I am not exactly sure what you mean with O'Connor's use of religion in society. But I can tell you that she was essentially interested in the cold hard realities of life and found writing a way to express herself. In a publication, "The Living Novel: A Symposium" she wrote, „I see from the standpoint of Christian orthodoxy. This means that for me the meaning of life is centered in our redemption by Christ and what I see in the world I see in its relation to that." Therefore all her stories are filtered through her beliefs.
To connect this with society, I think she uses religion and its role in society to criticize or to exemplify the role of religion in society. In "A Good Man is Hard to Find" she makes clear the idea that the grandmother becomes a 'good woman' only when her life is threatened. However, she was by society's standards a good woman who went to church each week. The reader can almost taste the irony presented in the story when the grandmother 'becomes' a good woman.