You cannot compare your situation (amongst "Southerners" but simlar to many rural communities in all parts of the US) with first cousin marriage as a normal routine occurence among Muslims.
Many of my ancestors are married first cousins. Three of my father's four grandparents were cousins to each other, two of them first cousins. The practice has gone back to nearly three hundred years that I can uncover, and I suspect it's longer than that.