Agreeing to disagree. Disagreements are even deeper amongst band members, as music is often all they have. To become a successful musician requires a lot of sacrifice, and an acceptance of the possibility of a life lived in virtual poverty, not unlike the vow Priests take. Their very sense of self-worth and identity are inexorably tied to the music they make.
There are many examples of inter-band squabbles: John and Paul, Ray and Dave Davies, The Don and Phil Everly, Phil and Dave Alvin, Dave Edmunds and Nick Lowe, Levon Helm and Robbie Robertson, Flatt and Scruggs, Buddy Holly and The Crickets, Roy Wood and Jeff Lynne immediately come to mind. There are thousands of others.