You guys can laugh at me, but I think the SEC unity thing is an indirect effect of history, from the Civil War through Reconstruction through the hard economic times that followed, through the civil rights movement, through today.
I don't mean this in a negative way, or a collective guilt way. Just that those experiences give Southerners, generally speaking, a sense of history and region that is much different than Northerners or Westerners have. That sense of region and being the guys getting looked down on brings a sense of unity and us vs. them that makes their fans see other teams in their conference as "us" even though, eg, Bama hates Auburn more than hell itself. It's still "us." They're more likely to be raised with a notion of the South as a region and a idea and family and their past. Hell, my people were in the mountains of Italy a hundred years ago, so my sense of the North is relatively recent.
I won't go on and bore you, but that's my back of the envelope assessment as a Northerner born and raised, but one who has read a little history and one who has traveled by car, side roads style, through the South more than a lot of Southerners have.