Thurman Munson and Reggie Jackson
These two were night and day, with Reggie bringing the flash and Thurman the grind-it-out heart, and they really didn't like each other. Apparently, Thurman wasn't the most open-minded dude, but he had no tolerance for Jackson's showboating (and refusing to run in practice).
Billy Martin also hated Jackson, so it was probably all just Reggie being Reggie. This threeway anger-fest did not stop the Yankees from winning the World Series in 1977, making them easily one of the most successful dysfunctional teams in sports history.