I despised the cocaine-fueled culture of the Cowboys, and have never liked Jerry Jones (although I do respect how he got to where he is). I have no problem with Jimmy Johnson, Aikman, or many of the amazing players that continually whooped our rear-ends in the 90s.
Maybe I see things differently than most, but it is rare that I hate a team just because they beat us. I appreciated the 49ers for the hard-fought games in the early 2010s, and the same with the Seahawks of that era. Lots of great games back and forth.
Even the mid-80s Bears have a lot of my respect. McMahon was a clown but he had talent. The rest of the team was a bunch of lunch-pail athletes that brought the iron with them to each game. I hated losing but respected their play. Sweetness, Singletary, Dent, Gault, Rivera, Duerson...
I get people hating the Packers and to me it's a sign of success. Do everything the right way and half of the people will be conflicted about hating you.