A GFCI outlet monitors the current
in the hot and neutral conductors and compares them. When no fault is present, the current is (obviously) the same. If the current is not the same, some is flowing somewhere else (ground) and the device trips.
Polarity indicators on boats predate GFCI protection. The "fault" light is connected between the neutral and ground. If everything is OK, there is no voltage difference and the light is unlit.
The "OK" light is connected between the hot conductor and ground (not neutral). Since there is 120 volts between the hot conductor and ground, the light is illuminated.
The problem with tis system is, it is actually a fault as far as the GFCI device is concerned because some current is flowing from the hot conductor to earth ground and there is an imbalance between the hot and neutral.
For this arrangement to not create a problem with a GFCI receptacle, the amount of current drawn by the polarity light must be less than the sensitivity of the GFCI device.
Fortunately, typical dock pedestal
boat receptacles are not GFCI protected, we rely on the outlets on the boat for GFCI protection but there is a move to require them on dock
pedestals and this will be a problem for many of us in the future.
If nothing has changed on the OP's boat and the receptacle in the yard has not been replaced with a more sensitive one, this is probably not what is causing his problem.