Seeing how cutthroat the film industry can be, it stands to reason that an actor or actress would be absolutely thrilled to be offered any role, but that's not always the case. Actors are people too, after all, and like everyone else, they can be offended, insulted or pissed off as much as the rest of us.
That being said, there aren't many stories of actors actually turning down a role because they felt insulted just through being offered it, but it does happen. This doesn't include people like Sean Connery, who famously turned down the part of Gandalf since his reason was not understanding the character.
For this list, only those actors who were offered a part in a movie that made them feel absolutely insulted can make the cut.
These good men and women of Hollywood have put in their time, they have paid their dues, and there is no reason they should simply take a role because it's available to them... at least, not when that role is little more than a middle finger pointed directly at them.
The actors and actresses who make up this small community are likely only a small vocal minority. Odds are, there have been hundreds, if not thousands of other examples nobody ever spoke about before.