There are two ways to proceed when you retune. You all seem to have one of them in mind and that one is retune, relearn your fingerboard, and then play a C when a C is called for. This is what I did when I retuned my bass in fifths, CGDA. I can play any song with the rest of the band because we are all playing a C when a C is called for.
Many people do it another way however. They retune and then continue to play all their songs the way they always have, ignoring the fact that their instruments now play some other note than a C when they play a C. They do not relearn their fingerboards. If you take this approach then either everyone in the band must retune the same way or the holdouts now have to transpose their music. And then of course the holdouts now have to relearn the transposed music. This is frequently the reason why whole bands want to tune the same way. But the other reasons given here are often true too.
This second approach may seem silly but in fact many band and orchestral instruments play a pitch other than the one noted on the music they play. Such instruments are called transposing instruments and bass guitars are transposing instruments already. It is relatively uncommon for bass guitar parts to be written out in standard notation but when they are they are written an octave higher that the notes that are actually sounded. An octave is a trivial transposition to make, of course. Most clarinets are tuned to Bb or A, they sound a whole step or three half steps lower than the notes written in their music, for example. That, like a drop tuned guitar, forces a non-trivial transposition if everyone is to play a C when a C is called for. Give a Bb clarinetist a sheet of music written for the non-transposing instruments in the band and he or she will have to imagine that every note is written one whole step higher and that the key signature has two more sharps or two less flats than it actually has. So there is precedent for this approach, odd as it seems.
