If the main panel breaker in the RV is off and the GFCI still trips, it is a ground to neutral short in the RV.
If the GFCI only trips when the main circuit breaker is on, and all of the other breakers are on, then there is leakage current between the neutral and ground when one of the branch circuit breakers is energized.
Turn main on, and all of the branch circuit breakers off, and test each branch by turning only one branch breaker on at a time to see which one causes the trip.
My guess is that it is probably the power supply/converter for the batteries due to large capacitors in this device or might be the refrigerator.
Kind of a common problem...
EDIT: Saw you posted an update and the GFCI is tripping when "all" breakers are off. If this includes main, then there is a neutral to ground short somewhere in the RV before the service panel if it trips when plugged into any GFCI outlet.
The other possibility is an issue with the cable/connectors.