Raised in Commanders country and currently living in Ravens country. As a kid in Northern VA, hearing about the Skins all the time wasn't as horrible as one would think.
There are a lot of Cowboys fans in the DC area. Cowboys Week during the first Gibbs Era would bring a ton of Dallas news all week long. There were even players on the Skins that I grew to like.
It was also great because the Skins scouts and GMs would come on this pre-sports radio show called SportsTalk and talk tons about the draft and about other NFL players.
As far as contributions from fans of other teams, I really like hearing different perspectives or perspectives from "enemy" territory. Even within a fanbase, opinions from someone living in Texas can be unique from those of someone in another state.
I also go to other NFC East teams' message boards to learn about players, injuries, performances in recent games, development and contributions coming from rookies, team turmoil, etc. ExtemeSkins, Giants.com, Warpath, and somewhat IgglePhans (that board format is difficult to read for me - if I knew of a dif Eagles board formatted like this one I'd read it more). Message boards are a great source of links to team articles if nothing else. I do the same thing with college ball (terps fan; visit ACC team boards).
If you're on a board long enough, you figure out pretty quickly who is a blind homer and who is informed, so there's definitely information to be gained. Every board also seems to have at least one member who seems to have an inside source to players or contracts and offer legit breaking news before the larger media can get it out there responsibly.