I don't really hate any sports teams, but a couple are on my radar, for different reasons.
1. The Chicago White Sox: as a Cubs fan, which you can see from my avatar, I'm supposed to hate the Sox. Except I didn't grow up in Chicago and didn't get exposed to that rivalry (see second point below), and as far as I'm concerned the game they're playing in the American League barely counts as baseball, due to the DH rule. So I just straight-up don't care about AL baseball and don't give the Sox a second thought unless it's inter-league play.
2. The St. Louis Cardinals: This is the rivalry I grew up with, the famed Cubs-Cards rivalry. I grew up in Springfield, Illinois, right between Chicago and St. Louis, and the town's baseball fans are split almost 50/50 twixt the two teams. Since I grew up watching the Cubs on my grandpa's knee, I'm a Cubs fan. I have no hate for the Cards - as a Dudeist, I have no room in my heart for hate. But Cards fans, on the other hand, can be jerks sometimes. I suppose any team's fans can be jerks, but Cards fans seem to be particularly good at it.
3. The University of Illinois football team (Fighting Illini): I don't care about college football at. all. And the only way you'd get me to a college football game is if it was in my back yard and they were giving out free Purple Kush. But I have a bad taste in my mouth about the Illini in particular because of an incident that happened when I was growing up. Back in like, 1980 (ish), the Illini were going to the Rose Bowl. For weeks, it was all anyone in Illinois (again, where I grew up) could talk about. "The Illini are going to the Rose Bowl! Oh Great Day in the Morning! My life now has purpose!" People were naming their babies Chief Illiniwek. Businesses were planning on closing the day after the game to accommodate all of the hangovers from celebratory partying that was going to take place. It was that big of a deal. Well whaddyaknow, they got their butts handed to them in the Rose Bowl, and the University of Illinois football program has been a disgrace ever since.
Honorable Mention: a local Catholic high school football team in Springfield, Illinois, which shall be referred to as SHG for simplicity's sake. Springfield has three public high schools and multiple private ones, SHG being the biggest. Since as long as anyone can remember, the public schools' football teams in Springfield have sucked eggs (mine went 0-35 across four seasons in the 80's), while SHG's football team has been dominant ever since Father O'Reilly coached the first team back in 1890, or whatever. The local newspaper, every high school football seasons, acts as if the SHG football program is the greatest thing to happen to Springfield since Abe Lincoln left town. Hand to Og, if the Cubs win the World Series, and the final game is on a Friday, the front page of Saturday's sports section in the local rag will feature SHG coverage. The Cubs might make Page 2, unless there was other high school football news that day.