Maybe I wasn't clear. The GFCI on the shore power inlet is integrated with the breaker. The breaker is between shore power and all internal outlets including the charger-source outlet. When the inverter is connected the charger and shore power are not, and the inverter's own GFCI trips unless the shore prower breaker is "off" (that's the part I don't understand). Turning off the shore power breaker does disconnect the shore power connector outside the boat (which is a European female plug and therefore not a potential hazard).

Your point about leakage here and there is worth checking out, but my real question was whether a GFCI on the same circuit with another GFCI is likely to cause a trip condition.

BTW the boat is basically off-grid. We keep it on a mooring and have enough solar to keep up. Since I owned it (starting my third boating season with this boat) I have never used the shore power connection except to run an electric heater or top off the charge during winter layup while on the hard.