The republican leadership is upset at King for the same reason they are upset at Trump. He's not using the buzz words that facilitate hiding the obviously racist policies of the republican party. They are destroying the cover for those who consider racism a minor issue in political discourse and can thus vote republican because the dog whistles allow a level of denial. But once the rhetoric no longer hides the racism, even those who are usually benign on the issue have to take exception to blatant racism if they are going to mingle with people who's lives are not neck deep in racist propaganda.
It's getting harder for "Joe the Plummer" to deny that a republican politician is a racist because they "don't know what's in his heart", when the politician's words scream racist and all the racist organizations throw the politician praise.