Is it wrong to use 2 GFIC breakers on 12/3, sharing the neutral, even if the breakers are on different phases?
The reason it's tripping is that the two GFCI breakers are feeding two circuits with the common neutral and there is no way for each of them to tell if a hot-neutral imbalance is due to a leakage (which should cause a trip) or current through the other breaker.

You need to either run separate neutrals or, as @tyson commented, use a dual-poll GFCI breaker.

BTW, running a MWBC on two separate breakers is against code. They must, at least, be linked to always dual-trip.