What do Alabama and West Virginia have in common?
One thing is that the rural cultures of both states, if not also their urban cultures, are largely derived from the culture carried into them by their Scotch-Irish settlers. See Cracker Culture by Grady McWhiney or Rediscovering the South's Celtic Heritage by Barry Vann. Of course there are other cultural influences, but those other influences may be more different than alike in the two states.
The stereotype that they are said to have in common could have more to do with the people outside the two states who hold that stereotype than with the people of the two states themselves, who are assigned the stereotype. Rural poor people are often very knowledgeable, even if without schooling. (Do not equate schooling with education. They can be the same thing, but need not be; either can be had without the other.) Presently, many rural people work in nearby factories. In former times most rural people farmed. Farmers had to know carpentry, animal husbandry, agriculture, spinning, weaving, sewing, and other skills. They often doctored themselves with medicines that they grew or collected from field and forest. They went to town on Saturday and to church on Sunday where they conversed with their neighbors, often thereby becoming well informed about current events and politics and government, and religion. They were not ignorant, even if many of them could not read and write. On this see:
Pudner, H. Peter. 1971. "People Not Pedagogy: Education in Old Virginia," The Georgia Review, 25 (Oct.), 263-285.
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It's difficult to know what aspects you are looking to compare without any context for your question. However, one similarity is that the citizens of both states are not held in high regard by the rest of the country. They both have a reputation for being simple, uneducated, or even of low intelligence. Of course, this is a stereotype (generalizing a certain trait, usually negative, and applying it to a group as a whole). Historically, some residents of West Virginia, known as hillbillies, lived in very rural, isolated mountainous areas, with few schools. Likewise, some residents of Alabama, considered the heart of the deep south, also lived in very rural areas with limited education. Both states were also very poor with little modern industry. In modern times, people who fit these stereotypes are becoming less common.