Brittle versus bouncy/flexy
Though I'm sure there are others, Bakelite is a phenolic plastic. Phenolics were phased out in favor of newer, more flexible plastics because if their brittle nature (anyone remember the Zenith ad where two identical radios were pulled off the table by their cords, sending them crashing to the floor--the Bakelite radio shattering, and the polypropylene radio bouncing?).
As such, if you have a Bakelite agitator, it will be very hard and brittle. Rapping (gently) on it will be like rapping on sturdy wood; it will knock but not provide bounce. Polypropylene (e.g., the PowerFin agitators in Maytags) is very flexible. If you had an agitator with detached fins, they would be easily flexed; if you rapped on it, there would be a very subdued sound and a fair amount of bounce back at you.
There is also the issue of wear--polypropylene agitators tend to retain their lustre, and Bakelite ones tend to turn dull and attain a very matte finish with age.
Of course, you can always try dropping the agitator for the definitive test ;-)