I think there exists a lot of contempt for teams that win "too much", yeah - see New England. Not really a team of yappers, but a hate-magnet nonetheless.
My personal opinion is that the type of characters on that Cowboys team made the hatred that much more acute. (But: At the time, I never thought I'd like Deion, but I rather like him on TV now...I enjoy hearing his opinions and I think he's hilariously funny at times. I don't mind Irvin, either. The one guy - not a Cowboy - I still can't stand is Shannon Sharpe. Yappy, yappy, yappy...still can't stand that guy.)
I don't think we have anyone really like that on this Packer team, but maybe I'm blinded by love or loyalty? I can't think of anyone in our case - is there someone you have in mind?