First in this situation, check Ground-Neutral continuity at the inlet, cord(s) disconnected. On 30A and 50A /125, check between the bent prong and the smaller of the other two. On 50A 125/250, between the straight prong and side contact. If a galvanic isolator is installed, jumper the two ground connections for the check. Make sure circuit breakers are on and switches set for operation from the inlet being checked. It isn't necessary to check multiple inlets. If continuity is found you must locate and isolate the connection.
This situation is coming up regularly and will be for some time as marinas upgrade. Improper G-N connections on boats are fairly common, and the adverse influence on corrosion and zinc depletion is often overlooked or ignored. I have seen a number over the years with the main G & N busses jumpered together and looking like original work. Or a land electrician has come along and thought it should be added. Improper inverter wiring and improper wiring of a 120/240V domestic appliance will introduce a G-N connection. This connection puts the ground wire in parallel with the neutral, an alternate path for the load current, as these are properly connected at the transformer or distribution panel serving the pedestal. G and N are to be connected only at the source of power, and the connection tied in only when that source is in use.
A galvanic isolator's monitor should not trip an ELCI device, as it uses DC which is not sensed by these devices. This test current does not flow to the pedestal, only across the isolator. I guess I shouldn't rule out an odd exception though. A test arrangement might be done with a 120V indicator lamp and a button, and this would trip an ELCI unless the lamp current is very small. An ELCI can be tripped by a combination of poor neutral connection, high load, and: A main breaker with reverse-polarity trip, or, an incandescent reverse-polarity indicator. Either of these will read continuity at the inlet. In the case of the circuit breaker the trip coil will have to be disconnected. An LED indicator will not cause a trip. In such a case, correcting the poor neutral connection may solve the issue.
And, the issue could be an actual live wire leakage fault. And something else that could give it a curve here, OP's location is shown as Gibraltar. Is this a N American or Euro wired boat, and is there a transformer installed?