An article from gossip site Nicki Swift describes this phenomenon (emphasis mine):

Celebrity feuds are fun to watch from the sidelines. You can passively root for whichever dog in the fight that you happen to prefer without having to get actively involved or stop anyone from coming to blows. But some huge celebrity feuds were actually made up—or at least blown out of proportion by the media. These celeb feuds weren't exactly real: they were either made up by the participants or by the gossip rags. After all, who really wants to let the facts get in the way of a good story about a feud?

Based on this article, I would call such incidents "made-up celebrity feuds." Perhaps "fake feuds" would be more concise. If you want to describe the writing about such alleged disputes, you could call it "fake feud gossip."

An article from gossip site Nicki Swift describes this phenomenon (emphasis mine):

Celebrity feuds are fun to watch from the sidelines. You can passively root for whichever dog in the fight that you happen to prefer without having to get actively involved or stop anyone from coming to blows. But some huge celebrity feuds were actually made up—or at least blown out of proportion by the media. These celeb feuds weren't exactly real: they were either made up by the participants or by the gossip rags. After all, who really wants to let the facts get in the way of a good story about a feud?

Based on this article, one could call such incidents "made-up celebrity feuds." Perhaps "fake feuds" would be more concise. If you want to describe the writing about such alleged disputes, you could call it "fake feud gossip."

Disclaimer: as noted in the comments, this is not a fixed phrase or a specific established idiom; rather, it is an description roughly borrowed from the above article.