Polyester doesn't shrink so there's no reason to prewash it. Besides, it would shred if not yet quilted.
For cotton batting, it depends on the type of batting and the look you want. Cotton batting with a needle-punched scrim, such as Warm 'n' Natural, will hold together for washing if you want absolutely no shrinkage at all. It doesn't shrink much anyway, though.
A cotton batting without needle-punched scrim must be handled very carefully to avoid shredding. Fairfield cotton batting benefits from pre-washing if you want to hand quilt it because it has a coating on each side. This coating works well for machine quilting but can make hand needling more difficult. To get rid of the coating you soak the batting in the washing machine and spin it out; no agitation cycle at all unless you want shredded batting! Most other cotton battings do not benefit from pre-washing and the batting cover instructions usually indicate they should not be prewashed.
I personally don't prewash any type of batting. The only reason I can think to do so would be if I developed an allergic reaction to the chemicals used to process a batting.