My gramps was a lifelong Cubs fan and rooted for the Sox in '05 because his entire remaining family (my parents, brother, and I) that he was close to were Sox fans and he (correctly) felt the Cubs would never win in his lifetime. He also didn't care about the rivalry as much as say, Cards-Cubs, because interleague hadn't been around for the vast majority of his life.
If the Sox ever want to "own Chicago" like a lot of us would love them to, they'll have to win over a lot of fair weather, bandwagon fans - or people that just like both teams. That's the way it is.