Yes, please keep real-world politics out of this.
In my new Champions campaign, the heroes are based in San Francisco. And one of the first news items concerned a hero team (Angel Force) forming in Los Angeles. The PC team (Golden Gate Guardians) disliked Angel Force immediately simply because the NPC team formed before them. I had planned to make Angel Force holier-than-thou, dismissive of the Guardians, too tough on criminals (taking the law into their own hands), probably start infringing on the PC team's turf, but haven't really needed to yet. There's no Rivarly on any character sheets, or Watched, just plain old roleplaying.
Now, if the PC team wanted to build, say, a base or team vehicle, and wanted to add Rivalry: Angel Force or Watched by Angel Force as a team-wide Complication, I think I'd be okay with that.