Here's more information about the community. It was the result of a religious cult. It wasn't a normal appalachian community.

http://www.brusselsjournal.com/node/4011

The Oneida Colony functioned, in effect, as a large-scale experiment in group-marriage, the governance of which ran to the bizarre. In Edgerton’s words, the Colony’s rules of promiscuous cohabitation “prohibited any lasting emotional attachments (including those between mothers and their children), and required all men, except Noyes and a few other leaders, to practice coitus reservatus,” or non-ejaculatory intercourse. Later on, Noyes imposed new strictures, according to which, “only older men… would be allowed to have sex with young… women,” whereas “young men… could only have sex with postmenopausal women.” These arrangements, which exist elsewhere only in a comedy by Aristophanes, produced so much revulsion that communal order broke down in open rebellion, with Noyes fleeing to Canada in order to evade charges of statutory rape.

“Duddie’s Branch” was an extremely isolated mountain hollow, home to two hundred and thirty-eight incestuously related people, who, while nominally English-speakers, “spoke to one another so rarely that for some time [Rena] Gazaway,” the anthropologist who studied them, “thought that many of them were mute.” The “Branchers” not only could not read or write; they could not even count change. They had no notion of the civic order and could not name for Gazaway the (or any) president of the United States or explain their situation as citizens of a county or state. The Branchers’ poverty and insouciance left them perpetually malnourished, especially the children; people defecated not in outhouses or trenches (they had none), but on the ground outside their shacks, in the perpetual mud where their louse-infested children played. The Branchers found it impossible to reckon kinship both from lacking the requisite terms and “because sexual relations were indiscriminate… and illegitimate births were commonplace.”