Okay, I did a little checking:
Bakelite is probably up to being boiled or autoclaved. It is said to be very temperature resistant once set.
Not sure about celluloid, but since table tennis (aka ping pong) balls are made from celluloid one could run an experment using one.
Natural materials such as bone, ivory, wood - don't know. I would be very nervous about exposing wood to high temperature steam or hot water howerver.
If you want to see what barbicide or clippercide might do to celluloid, spray, dunk a ping pong ball and let us know.