AC 91-85 states:
"An automatic altitude-control system should be operative and engaged during level cruise, except when circumstances such as the need to retrim the aircraft or turbulence require disengagement. In any event, adherence to cruise altitude should be done by reference to one of the two primary altimeters;"
Most POIs will interpret should as shall and will Approve the RVSM ops manual accordingly. At the end of the day it will depend on what your POI or FSDO approves and what your Operations manual states in its procedures section which is required regardless of what FAR you operate under. This is how you are approved to fly the aircraft.
At our operation I made it mandatory on all part 91 aircraft and 135 aircraft that the aircraft be flown on autopilot in the transition and while in RVSM but thats just us.