Often in an RV, the receptacles and the converter are on the same breaker, so you need to turn off the converter with a switch you insert into its own black wire before it gets to that breaker, so you can leave that breaker on and have the receptacles working from inverter.
If, say the outside receptacle in the RV is wet from washing the rig, or whatever, the RV's own GFCI will pop. If the inverter's GFCI pops, but the RV's does not, that's interesting.
If home, you can run a long extension cord from the Rv shore power cord via adapter, to your stick house bathroom GFCI and see if it pops. If so, the Rv has some sort of ground fault anywhere along the way from the plug in the bathroom to the adapter 15/30 to the shore power cord to the power centre, to any of the branches, to anything plugged into any of the receptacles.