Unhook the neutral and hot (load side) from the GFCI breaker and measure the resistance (VOM and/or megger) between the neutral wire and the neutral bar -- it should be open.quote; The neutral is not shared.
Are you absolutely certain that there is NO OTHER circuit using the neutral wire? Does the neutral go DIRECTLY to the panel box so you can be sure of it.
In my limited experience with residential wiring (I am not a pro in that area), it's not uncommon for neutrals from different circuits to be intentionally tied together (obvious DIY hacks), but in that case, a GFCI breaker *should* always trip with a load on either circuit, and in theory possibly even without any load at all -- depending on the design of breaker.
I still think what you describe sounds like a flaky breaker. Probably a manufacturing defect...