This problem is quite obvious once the nature of so many generators is learned. A 120 volt generator can make 200 volt spikes. That is ideal power for 120 volts electronics. And problematic for near zero joule power strip protectors.
That 200 volt spike can mean current outgoing on the generators hot is connecting to safety ground via lightly triggered MOVs.
Furthermore, those power strips must never be used where 120 volts might create tens of thousands of tiny (less than 330 volt) spikes all day. MOVs are only designed for one or a few large surges. Quickly degraded to ineffective when confronted by constant noise spikes.
Degradation cannot be reported by the "protector good" light.
Anything that power strip protector might do is routinely done better inside electronics. View numbers. How many joules does that power strip claim to absorb? Hundreds? Electronics routinely convert a hundreds or thousand joule surge into rock stable, low DC voltages. Surges are safely consumed to power semiconductors. Same surge can destroy that near zero joule (with massive profit) protector strip.
GFCI trips if the current outgoing on the hot prong is not exactly same as current incoming on the neutral prong. If that current leaks elsewhere via power strip MOVs, then GFCI must trip.
Best power strip has no protector parts and always has a 15 amp circuit breaker.
Other reasons inside a power strip can explain that trip.
Meanwhile build a diagnostic tool: a simple GFCI tester. A 20K adjustable resistor in series with some fixed 1/2 watt resistors connects from hot to safety ground. Resistor is adjusted so that 3 milliamps (hot to ground) cause no trips and 6 milliamps (or more) causes a trip. Now a tester can report what current actually causes a trip. And even if the GFCI is working properly. Those store bought GFCI testers do not provide the same adjustable test and perspective.
If that tester with power strip causes a GFCI trip (when resistor is only at a 3 milliamp setting), then you know how much current is leaking through that power strip. Do same test only with a laptop and that tester. Apparently power strip leaks much current - but not enough to trip a GFCI by itself.
Finally, some GFCIs are also more likely to trip (more sensitive) when AC noise exists. Also get a line filter (that is normally found inside all electronics) from electronics supply house (ie Digikey, Mouser, Allied, Jameco, etc). Build a little box with that filter located sit between the generator and appliance. Does that filter stop GFCI trips? Then know its GFCI is also noise sensitive. And know which appliances are creating too much AC noise. That line filter is also a powerful diagnostic tool.