...he has the right to poke a little fun at other rural white guys....
To be completely fair, though, there isn't anything about the word "Alabama" that makes its use merely to refer to only rural white guys, nor is rural white guys a race per se. The word "Alabama" can also include black guys and urban guys [in theory] since Alabama has a lot of non-white persons, even rocket scientists. In practice, I strongly suspect the stereotype of brothers and sisters has more to do with population bottlenecks than race--to include relative isolation in the past or lack of availability in sparse communities. So there may be very little access and availability of peers in some areas for youth [or in the past] and that may carry some larger probability of breeding with a distant or close cousin, creating endogamous communities.
Example:
Abstract
A survey was conducted of 324 members of the Cajun isolate of Southern Alabama. Tradition and appearance suggest that this population of about 3,000 are not entirely White, Black, or Indian but constitute a triracial community somewhat reproductively isolated and inbred. The earliest American settlement in the area, along the banks of the Mobile and Tombigbee Rivers, lay between Spaniards to the South and Indian tribes on the other sides: Creek, Choctaw, and Cherokee. Physical measurements are reported for 71 adults, plus color of skin, eyes, and hair. X-rays were taken of wrist and ankle bones of some 253 children. Red blood samples were typed on adults and children, and haptoglobin, Gm, and Gc types were determined from serum. History and physical examinations were also made. Physical measurements and observations suggest predominantly White ancestry, and D2 analysis confirms this, with least similarity to Indians. Analysis of serological traits implies almost 70% White, almost 30% Black, and very little Indians genes. Few defects of clear genetic etiology were discovered. Growth patterns judged from X-rays appeared normal. All genetic loci testable were in Hardy-Weinberg equilibrium except Gc. While history and some common surnames suggest endogamy in the past, the medical and serological findings, plus some additional surnames, indicate that the isolate has already been largely diluted or dissolved.
https://www.ncbi.nlm.nih.gov/pubmed/888930
So such communities may have been endogamous in the past, creating such Alabama stereotypes along with other communities (such as rural whites), but in the present such communities may have lost those characteristics (diluted) because there is a lot of access and movement today..much less isolation. The stereotypes may live on, though. But still....there is no reason such statements apply to only whites or that its theoretical application to only rural whites in Alabama makes it racist.