Like the other person said, Coolio didn't like Amish Paradise for years. He eventually realized he was being a dick about it and apologized to Weird Al.

Prince despised the idea of parodies for his songs and at one point Prince's management told Al to not even look at him while they were both scheduled for the same show or something.

Paul McCartney rejected a parody called Chicken Pot Pie on the grounds Paul (and Al too) is a vegetarian, but was otherwise down to let him do parodies.

Lady Gaga's management DID NOT want weird Al to do Perform This Way, but Al released it anyway and Lady Gaga loved it.

TBH, these are things I remembered off Al's Wikipedia page.