Chase --
Thanks for raising the point I meant to save for another time. Since we're talking about mass politics, I hope none of of seriously believe that a small group of men have a master plan to manipulate the outcome of elections.
Since the middle of the 19th century, Southerners have been regarded as an undesirable ethnic minority. James Webb in Born Fighting: How the Scots-Irish Shaped America believes this prejudice goes back at least another century.
Since women couldn't vote during much of the period under consideration, it's not reasonable to consider the lack of female candidates. As for the other two minorities, a news survey taken in Detroit MI in 1960 asked readers to identify the least desirable ethnic groups. White Southerners (AKA "rednecks") easily won over the other groups you identified.
That kind of prejudice should explain why Southerners weren't considered viable candidates for national office during this era.
Webb presents a great deal of support for this point. It's really not necessary, since almost anyone who grew up in the United States is fully ware of the cultural stereotypes. Note also that we can use the term 'red neck' in a post, but not other ethnic slurs.