A GFCI works by comparing the current in the neutral line with that in the hot line. If that in the neutral line isn't the same as in the hot line, the current is returning through something else, possibly a human. If there is even a tiny difference, it trips.
Ground and neutral are tied together at your house or campground's main power panel. They should NOT be tied together within your boat or RV. If they are, some of the return current will return on the ground line instead of the neutral line and cause the GFCI to trip.
I suspect this is your problem... neutral is tied to ground somewhere within the Airstream. Just because it happens with all the breakers shut off doesn't necessarily mean that it's in the main power panel.