No, I think you can be a fan of 2 teams only if they're in different conferences, but I still can't see somebody being a Giants fan and a Chargers fan. That Eli trade (if you're a chargers fan) should make you hate the giants on principle alone.
Like in baseball I grew up and I'm still a huge Cubs fan but I like the Padres because I live here and they're always on. But, when the two teams meet, I don't root for the Padres.
Who do you root for when the Eagles play the Chargers? I never got into football till I live in SD so I've always been only a Chargers fan.