It really depends. Back in the early 90s, I wasn't using the internet and I wasn't exposed to how horrible other fanbases can be. So I had no problem pulling for the Bills when they got there (I have family in Buffalo, they had an exciting offense, they faced the Cowboys twice, etc.) I even kind of liked them when they had Doug Flutie running the show toward the end of the 90s. Nowadays? I've heard enough of their fans' BS online that it would be a tough pill to swallow cheering them on in a Super Bowl. As for the other division rivals, I didn't really learn to hate the Dolphins until "Run, Ricky, Run" and the obnoxious hoard of Fins fans that I saw invading this forum all the way back in 2002. The Pats narrowly missed the playoffs but it was fun watching the Pats take the Dolphins down with us. And don't even get me started on the Jets.
Having said all that, there are other factors to consider. Are there any ex-Patriots playing for/coaching these teams that I'd like to see get a ring, even if it's with the enemy? Is one of the rivals facing an NFC team that I hate even more (currently the likeliest would be the Giants)? Is there a player on that NFC team that I can't stand? It's a tricky thing because right now virtually every team's fanbases hates ours, and I tend I return the sentiment, though I don't think Saints fans hate us that much.
The internet has kind of ruined me, because I've experienced all the hate from all the teams, and it's given me reason to loathe way more teams and their fans than I did in my pre-internet days. The Patriots' success (as well as Boston sports success as a whole) has drawn more of that contempt, from more people (look at Deadspin, their entire staff hates the Pats and that includes a guy who grew up in Massachusetts), and it's hard for me to overlook that. I can't bring myself to cheer on behalf of fans who call our team cheaters and who wish injury upon our players, and that's the majority of the NFL. When the Pats aren't in the SB, I just root for who I perceive to be the lesser of two evils (and usually the eviler team wins just to irritate me).
I'd never say never when it comes to pulling for a division rival in the Super Bowl, but it'd take a lot to sway me. I consider myself very fortunate to have not had to face that dilemma for a long time. I root for the Patriots unconditionally, and root for the Saints if the Pats are out of it (or even the Niners with Garoppolo, I'm not concerned with the trophy count). Everyone else, it just really depends.
