Shore power issue on 1990 Jefferson Monticello.

I guess by GFI you actually mean that your marina installed a GFCI device (Amps are irrelevant in this respect) in a pedestal which previously had none.
If so, it implies that you have a current leakage somewhere onboard - and yes, that can happen also with all internal breakers off.
It could well be that everything worked just fine before, with no GFCI on the supply line, but now the GFCI snapping is simply revealing an electrical problem that was already there, unbeknown to you.

Regardless, chasing electrical dispersion requires an understanding of what that is, an appropriate clamp meter, and a fair amount of patience.
And since you specify that you hate electrical problems - not that anyone like them, mind, but you wouldn't say that if you'd be used to chase them - my suggestion is to use your wallet to fix this one.
I.e., involve a marine electrician!
Guiding you through a possible troubleshooting sequence from our armchairs wouldn't be easy, and certainly cumbersome for you to follow an "if-then" process that might well involve several steps.

PS: one rather common possibility, that could fix the problem easily if you're lucky, is a worn out shore power cable, and/or its plugs.
If you can borrow another one (known to work fine, obvoiusly) from a neighbour, the marina, or whatever, you could try to swap it.
If that stops the GFCI from tripping, you have found what you should replace!
Other than that, the current leak is somewhere onboard, which brings us back to my initial suggestion...

This has been discussed a few times on YF. Some searches can offer lots of reading.

Bottom line, green wire has current on it tripping the service breaker.

So, not all is off onboard; including the breaker panel night light or digital meters.
There is return current on the green wire, supposed to be on the white wire only when connected to shore power service.
Also, try unplugging everything, including appliances, especially the laundry machines.

After everybody is sure the inverter is off and disabled, Un-strap the green & white wire on the inverter(s), for testing only.
Un-strap the green & white wire on the gen-set(s), for testing only.

Your electrician may want to look at the inverter first. This has been found to be an issue a few times.

This is a fairly common issue with more and more marina upgrading their electrical system. The problem is almost always caused by a Neutral to Ground connection somewhere on the boat.

a frequent culprit is a non marine inverter. Off grid and RV inverters permanently bond N to G but marine inverter only do so while in inverter mode. So, if you a non marine inverter, start there

next would be any major appliance, especially older ones. Washing machine, dryer, stove, oven, fridge etc. unplug them one at a time. If hardwired, disconnect the wires.

the reason you can’t diagnose by turning off breakers is that single pole breakers only turn off the hot, not neutral.

The generator should not cause the issue even though they bond N and G since the rotary switch or circuit breaker should disconnect N. Unless someone did some creative wiring

I think it's more likely that the problem doesn't exist on genset for the very simple reason that the boat doesn't have any GFCI device at all.
If she had one, it should have tripped also before the marina fitted one in the dock pedestal.

BTW, if that would be the case, this troubleshooting "forced" by the new marina safety upgrade is a great opportunity to fit also a GFCI onboard, upstream of all AC components and hence working with both dock and genset AC power.

It is amazing how often we found that creative Bubba was on board.
Many OEM panels with the sliding thingies to block dual pole breakers have these issues, white & green wires always tied.

I remember a lil/ole Catalina snail boat , without a gen-set, that was intermittently tripping a service GFI pedestal.
Owner kept blaming the battery charger.
There was a factory strap from N to G behind the panel. Think boat was built before GFI was getting popular.

I assumed a typo in the OP post, but now that you also use GFI rather than GFCI, I'm wondering if it's my English that is poor.
Or are the two acronyms used indifferently, in the US?

GFCI, GFI, CGFI and more.
Were so used to our lil GFI outlets in the galley, head and other wet locations, we naturally call everything GFI.
But it is not that simple any more;
Shore power breakers with ground fault tripping, ships inlet breakers with ground fault tripping, NFC, ABS, ABYC, FCR, UL and others have so many different names for these devices, it gets confusing talking to the guy across the dock, much less across the pond.
They are ground fault thingies;
On the dock, ships entrance or in the head is all most of us need to know to chat about it.

There; the mad man from the swamp has spoken (typed), more mad stuff again..

You've got some nice headphones there.
Did I miss the last model from Bose?

Latest model From Josie (wife).
On a calm solar night, I can pick up traffic from Mars...


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