They hate Cal, like Tubby, and love Rick. They don't like one and dones.
I don't think their dislike of UK has much to do with us as fans.
Do you mean Goodman and O'Neill in particular, or just in general? We have long been disliked, by the public at large and especially by media types. Only Duke can rival us for widespread hate, and they are relative newcomers. I think it does have something to do with the fan base. Really, these reasons come to mind:
1. Calipari/One & Done. He is a lightning rod, a polarizing figure. Always was, dating back to the Carnasecca story. Now you add the one and done to that, it's only worse. And he's at Kentucky, again, makes it only worse.
2. Racist history. This has been beaten to death. But at some point in the late 80s into the early 90s the idea began to take shape that Rupp was a virulent racist, and the '66 title game began to stand for something that it did not in real time. Every story needs a villain, and the crop of journalists that came of age in the 1970s and later latched on to us as the villain. By now, this story is crystalized as accepted gospel. It no longer matters what the truth is.
3. Cheating history. It doesn't matter that we've been clean for almost 30 years. The point shaving scandal in the early 50s, and the Emory matter in the late 1980s define us for a whole group of people.
4. The fan base is "Exhibit A for excessive behavior". That's an old Bob Ryan quote about UK fans. We are crazy. There are other very large, very crazy fan bases, but the only one that really rivals us is Bama's football fan base. We will descend like a plague on any writer - or referee - that dares to offend.
You add all that up and it paints a picture of a school & fan base that has its priorities all out of whack - where literally anything is acceptable if it means more wins. Anyone looking into the matter in any detail would come away with a different conclusion, but people are lazy, and want to talk in vague generalities.