As BigRedBass implied, at a certain level it is about the professionalism of the band and being a pro. This remark is in no way a put down of anyone fortunate enough who does not need to earn money from their playing
If fun is one of the most important factors, or you are a gigging performer who is booked up, or you are in demand enough or even famous, than one can easily say no to playing music you might not like.
I have joined bands I didn't like the style of at first, and ended up being in them for years and having a rewarding experience. I have also been in bands (very recently) that I liked the music and was making money but the band was run so unprofessionally that it turned out to be a nightmare and I won't play with them ever again, for love or money.
For better or worse, bands are like families who almost never stay together anyway, at any level, from famous to totally unknown and unpaid. I think experienced players factor this in and decide if the money or the perks are worth the time and effort.