There have been some posts going around about fandom in conferences (i.e. this one from Big Ten country), so I thought I'd give my two cents.
There is a contingent of SEC fans who see football and conference solidarity as rooted in the Civil War. KevinHog from Arkansas Expats did a great job of explaining that side of the story. Unfortunately, a lot of people assume that SEC pride is solely out of Civil War era sentiment. See this article from Oklahoma for an example of that viewpoint.
I'm here to tell you that it's not true. I am an example of an SEC fan who never thinks about the Civil War on game days. I don't refer to the Civil War as the "War of Southern Independence," either as the columnist from Oklahoma seems to think everyone calls it down here (or the "War or Northern Aggression," or any other such phrase). I am one of many fans in SEC country like this, and I feel that needs to be said.
All of my ancestors came to America well after the 1860s. My parents moved down to Florida from elsewhere when they were children. I grew up in suburban Orlando, which is about as far from capital-S South as you can find in the conference's footprint outside of Miami. You don't have to have a story like that though to be like me in my fandom. I knew plenty of students at UF who were from capital-S South areas of Florida (yes, they absolutely do exist) and who never once brought up history or swore at "Yankees."
As the population of the country has drifted towards the Sun Belt over the last 50 years, the southeast has become more and more urban. It still retains many of the things that make it Southern, but the percentage of people who view the country with a Civil War mindset falls with every passing year. The number of SEC fans that don't also grows with every passing year. I live in Charlotte now (ACC country, I know), and it's hard to find people who grew up here. The same was true in Orlando. In either city, the only time I hear people talk about "Yankees" other than the baseball playing ones from New York are either when they're joking or they're sports talk radio caller loons.
To the best my knowledge, the "S-E-C!" chant that has become so well known didn't come out of a Civil War mentality either. As far as I know, it first came about in SEC championship games. Since the conference had one game where the winner was unquestionably the champ, the fans of the winning team would chant the the conference's initials as a taunt to the losing team and fans, signifying their victory. It just spread from there because S-E-C is both fun and easy to chant.
I know my experience is colored by being from Florida, which is the least Southern of the SEC states and schools. Even so, the last line of the no longer played verse to the UF fight song, "Orange and Blue," encourages the Gators to fight on because "Dixie's rightly proud of you." I have an mp3 of a recording of the full song with the band and glee club from the early '50s, and the instrumental sections include the tune "Dixie." Every last one of the SEC schools has deep ties to the old South.
Not every last SEC fan does though. There are plenty of fans that simply think of football as football, and I'm one of them. Though our voices aren't usually heard as loud, I just wanted to speak up for once.