It could be faulty GFCI breaker but most likely is the fact that you are sharing a neutral between the two circuits (branch circuits). It is OK on a non-GFCI protected circuit; however, for a GFCI breaker to operate properly, it needs to have a dedicated neutral attached to it. Sharing neutral between those two circuits causes “leaks”, makes it unbalanced and results in nuisance activation / tripping of your breaker.
Simply put, a single pole GFCI breaker is not designed to protect multi wire branch circuit. You either need a double pole GFCI breaker, which can be quite expensive, or replace your single pole GFCI with a regular circuit breaker and properly install GFCI outlet receptacles at both ends of the branch circuit.
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