Absolutely not. In fact, I think it's doing yourself a disservice if you ignore the non-Protestant Southerners throughout history. There's a great excerpt from Robert Rosen's The Jewish Confederates that describes the hardships faced faced by Jews throughout the Confederate States. And I have no doubt in my mind that yes, these people, too, classified themselves as Southern.
Comedian Aziz Ansari, son of Indian immigrants, grew up in South Carolina. I think he does a damn fine job of explaining life in the South. I think he (and Rob Rosen from the link above) brings up a great point, too: worrying too much about someone's religion or race or background is thinking too much into it. In the end, it's all about love of your region, its food, and respecting your elders.
i've been really in to Hugh Acheson's two books - they are amazing!
http://www.amazon.com/The-Broad-Fork-Recipes-Vegetables/dp/038534502X