Yes, I'll play.
Pats apart, the liking for other teams is limited and conditional.
When I first watched the NFL, I liked the Chargers (Dan Fouts, Air Coryell, yeah!!) then I had a soft spot for the 49ers (need you ask why?) Especially when the Pats were nowhere, it was nice to have a team you liked in the play-offs, the more so when so many of the teams you really hate were being successful. But that liking has now disappeared. My dislikes are much more permanent (Washington, Dallas, Oakland, Pittsburgh, Indianapolis).
Now I somewhat like Cleveland because of Romeo and the honest, blue-collar fan base. I have a lot of respect for the Panthers.
The only originality I'll claim is that I don't have a particular hatred for our divisional rivals. If (heaven forbid) we were out of the playoffs, I'd want any AFC East team left to do well (hateful though the Jets and Dolphins trolls here certainly are).