Usually the fridge 120v plugs into a receptacle at the back of the fridge near the outside of the rig which you get at by removing the outside vent cover. This is below the fridge vent cover on the roof.
Water into the receptacle there can cause a GFCI to pop, but usually water doesn't get there. That receptacle the fridge is plugged into might be part of a receptacle string that includes an "outside" receptacle, which is more likely to get wet.
You can unplug the fridge 120v at the back and use a separate long 120v extension cord to a stick house GFCI receptacle like the bathroom's and see if the bathroom GFCI pops when the fridge 120v is turned on. Yes? Now use the same bathroom GFCI to plug the rig shore power cord into using that same extension cord but with the fridge unplugged from its rig receptacle. No pop? Ok the fridge is guilty.
