There are obviously teams that I hate for no good reason other than that they are traditional rivals and/or division competitors of my favorite teams. I will put those to the side and focus on teams I like/dislike due to reasons unrelated to that.
I am a rare bird in that despite having not ties to the New York area, I find the Red Sox and their fanbase more hateable than the Yankees and their fan base. To me the Yankees are pretty honest and transparent about who they are: they're the most successful team in MLB history, they have a ton of money, and they're willing to spend it. They own that identity. In contrast, the Red Sox do literally the exact same thing (and are the most successful MLB team of the 21st century) but for many years were celebrated in the press and in pop culture as loveable underdogs. That annoys me.
The Cardinals fanbase is terrible and full of itself - the team itself is pretty admirable. If I owned an MLB team I would seek to hire veterans of the Cardinals front office for scouting and player development roles. But I hope to never speak with a Cardinals fan about baseball ever again.
Speaking of front offices I admire, how about those Tampa Bay Rays. They do incredible things on a shoestring budget. And apparently the front office people there are just as underpaid as the players, so if you are say an owner or GM of a team that underperforms in drafting or player development, you could probably hire a bunch of those people! Beating their current salary won't be hard! But I digress.
When I was growing up in Chicago, the MLB team I had a soft spot for was the Montreal Expos. I just thought it was so exotic that there was a team in the French-speaking part of Canada, playing in a goofy stadium with a goofy name with French play-by-play guys using goofy French baseball terminology like "roulant" for a ground ball. I was fascinated by the very existence of the Expos. I had no idea that one day both myself and the Expos would end up moving to the same place.
You know what's a team that most people never thought about until a few years ago? The San Diego Padres. You either never thought about the Padres, or you had mild warm feelings about them because of Tony Gwynn being so darn likable. Recently, Padres fans have managed to erase pretty much all the good will that Tony Gwynn earned that franchise.