I have at least four GFI protected circuits in my bus, and they don't trip when running on my Yamaha 3000 iSEB (what a name to type). GFI circuits trip when there is a current difference between hot and neutral, the presumption is that stray currents are going back to ground. Usually the problem is the GFI outlet, but there is a potential issue with the Yamaha - it floats neutral with respect to ground, and code requires that the power source bond neutral and ground - so you may have a neutral/ground bonding thing causing a too-sensitive GFI outlet to have issues. You can make a bonding plug for the 15 amp outlet on the generator that ties neutral to ground, you can do it inside the twist-lock plug or you can take the generator apart and do it inside the generator panel. I would think about that.
Brian