First, I am using 12/3 romex feeding 2 new circuits to a pool area, for fans and ceiling lighting. Because of the rule, under 10ft from the pool water, you must use GFI's, I installed 2 GFI breakers. With 2 GFIC breakers in a small 220volt sub panel, when I turn on either breaker by itself, the breaker stays on. But when I switch the 2nd breaker on, they both trip. Doesn't matter which breaker is turned on first, the 2nd breaker will trip both. Because the fans today, draw such small power, and the ceiling lighting is all LED's, I am going to load every thing to one #12 wire and check the amp draw. If the amps are within a safe margin, I will then just use 1 GFI to protect the whole new install. I am not to crazy about running a new romex 12/4 or 12/2/2, as its sometimes marked, with 2-hots and 2-neutrals plus ground. Is there a way to share a neutral with 2 GFI's 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.