Totally against it. We get that a lot here in NY with the multiple teams in the same sport. Even beyond that, like your situation, I really am bothered by. I guess to me the test is...Do you take bragging rights with both teams? If the Cowboys are your team but you enjoy watching Dallas thats fine IMO.
I love sports so when my team is out I always find a team I want to win it. That being said when they do or don't win it thats it. I certainly wouldn't take any pride in it or talk shit to anyone about it. I could probably rank teams in each sport but I live and die with my 1 team. Another team I like to watch winning takes zero of the sting out of my teams failure.