Exaggeration-prone outsiders. In the 1880s and 1890s, writers such as Mary Noailles Murfree and John Fox Jr. traveled across Appalachia, looking for "local color," and overstated the degree to which mountain populations lived in isolation. During the same time period, missionaries reported pervasive ignorance and poverty, with large families living together in ramshackle cabins. The notion of widespread inbreeding was at least in part the result of crude assumptions about how these isolated forest people might have been perpetuating their communities.
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Stereotypes about West Virginian breeding practices have long been linked to the state's poverty. When Eleanor Roosevelt visited West Virginia mining towns in the 1930s, national newspapers ran pictures of rundown shacks and barefoot kids in rags, which left a lasting impression of the state as a backwater. West Virginians became the prototypical "hillbillies," and incest served as a crude "scientific" explanation for their downtrodden social condition.
Personally, I have a different explanation for that stereotype.