Now that I think about it you are probably right about the Royals. A rivalry like somebody said is when there is a buzz in the crowd and between fans and in the media. Remember when newspapers were a thing and there'd be page after page of Sox versus Cubs stuff? All over the sportscasts on chicago channel 9, 5 and 2? Folks, the Sox only rival is the Cubs even if one has to be cool and say the rivalry does not exist. Look at the all-time results in the series? Very close. Even when it was a once a year exhibition game it was huge until the clubs started to play their minor leaguers in the game. For a while, Sox vs. Cubs midseason exhibition game was a thing in which the guys on the big league roster played the whole game.
Cubs Sox rivalry, yes. All other series, no. There may be deep concern for certain series against Central teams but a rivalry? No way. How bout a cheap ticket since they play those teams 19 times a year.
Just my take.