I'm a Pittsburgh Steelers' fan, and my dislike for the Cowboys was bred in the 1970s. Having seen George Atkinson's malicious hit on an unsuspecting (not to mention out-of-the-play) Lynn Swann, my impression of Dallas has always been based in that one dirty play. I know it's not how they are now, but it has been in my mind from childhood, so that's my instinctive reaction to Dallas, and I have to fight against it constantly.
Having said that, I hope that I can be objective when answering your question about their fans, so here goes: Along with the New England Patriots' fans, Dallas Cowboys' fans (not all, and obviously not you, but MANY of them) are "fair weather", "bandwagon" fans. But in particular: Those with no allegiance to any NFL team are bombarded with the Cowboys' self-proclaimed hype of Dallas being "America's team."
And, since New England has been so good recently, and they ARE, of course, called the PATRIOTS, the perception is that it is somehow "un-American" to not root for the Cowboys or Patriots.
So while I don't necessary hate the fans who genuinely root for the Cowboys, I DO hate being called less of an American simply because I do not root for them or the Patriots - who, incidentally, have finally been PROVED to have cheated my Steelers in the 2002 AFC championship game.
It's just like with Yankees' fans: Since most of them are bandwaggoners, you never can be sure who really roots for the team.