There are plenty of reasons to hate teams that have nothing to do with those teams having an unfair advantage.
You hate the Cowboys because Troy Aikman is somehow on the top FOX announcing team, and is as biased an announcer as we've ever seen. Plus, Jerry Jones is essentially one of those fans who thinks he can do a better job than NFL GMs, except he's a billionaire so he actually bought a team and gets to play at GM.
You hate the Redskins because:
You Read This Article about their owner.
You hate the Patriots because: In the eyes of the media, they can do absolutely no wrong. They're smarter than everybody else and even when the hoodie fucks up he's brilliant.
You hate the Raiders because: Their owner is an undead monstrosity:
You don't need to tilt the playing field to make teams hateable. When you add to the fact that everybody's going to hate their division rivals, the fact that the media and asshole billionaires make certain teams eminently hateable is enough.