I don't doubt what you are saying, but as a Badger fan, I always try and treat visiting fans well when they are in Madison, win or lose. The most crap you are likely to get is at the game itself, but that is usually just in fun. At the bars, I would think people would treat you better. Of course if you are being a cocky jerk, most aren't going to be real nice. As much as I like to hate the Gophers and other teams, I can appreciate anyone who spends the time and money to travel and cheer on their teams. I have traveled to most of the other Big Ten cities for games, and 95% of the time, the visiting fans are friendly. No matter where you go, there are jerks, but ignoring them usually works best. If I see Gopher fans out on state street after the game, I usually thank them for coming, and hope they have a good experience.
As far as bars on State Street, most people try and cram into State Street Brats, it is usually way too crowded. I would recommend the Iris Pub or 608 for a more laid back experience, or Whiskey Jacks for something more upbeat.