Flannery O'Connor's "Good Country People" is probably her most widely read work and plenty of fine articles have been written on this short story. You'll find that eNotes has several bibliographical references in third link I've included below.
The 1990 article by Lisa Babinec, in particular, may provide some information on the societal elements of the short story.
I have found Robert Brinkmeyer's 1989 work The Art and Vision of Flannery O’Connor to be a helpful study.
Carter Martin's 1969 work may also help with the societal elements of the story (The True Country: Themes in the Fiction of Flannery O'Connor).
Ralph Wood's 2004 book, Flannery O’Connor and the Christ-haunted South, should also be a useful place to look for information on this subject. His essay focuses, as I recall, on the subject ofnihilism in the story.
Likewise, nihilism is the concern of Henry Edmondson's 2003-2004 article in the Flannery O'Connor Review, “‘Wingless Chickens’: ‘Good Country People’ and the Seduction of Nihilism."
Speaking of the Flannery O'Connor Review, students of O'Connor should certainly thumb through these journals as part of their research.
Finally, students should also look at O'Connor's surviving correspondence, which frequently contains her own thoughts on her work. Please see C. Ralph Stevens, ed., The Correspondence of Flannery O’Connor and the Brainard Cheneys (Jackson, Ms.: University Press of Mississippi, 1986).
Hope this helps.