Only possible issue is that some generators need a neutral-ground (safety earth) connection to satisfy surge protector/EMS systems. They will throw a fault code and shut down power if neutral and ground are not properly bonded at the generator.
Side note: A Surge suppressor/EMS system, either portable or built-in is a good thing to have to protect the electrical stuff inside your Airstream from surges, spikes, over-voltage and under voltage on the shore power cord. Search the forums for a discussion and a wide range of opinions. IMHO, I don't leave home without one in the AS system. Heck, my power fluctuates enough at home when I plug into the 30 amp RV outlet there I still use one at home...
The reason this happens is that, by design and the National Electric Code (NEC), the AC power return (Neutral, typically white wire) and the Safety Earth (green, bare or 'ground') wires are NOT connected inside the Airstream. The shore power cable carries these wires separately out to the plug, and the box or receptacle you plug it into is required to provide the connection between ground and neutral at the breaker box.
Most generators, either inverter (relatively quiet) or contractor type (the really noisy ones) have a "floating neutral" setup. The neutral and ground are NOT connected in the generator. There is an easy fix:
Buy a "Neutral bonding plug" or build a standard 3-prong plug with the neutral side (wider blade of the two, silver screw, white wire) tied to the ground connection (longer U-shaped or roundish blade, green screw, green wire) inside the plug with a piece of #12 wire. When you use the generator to power your Airstream, stick this plug into ANY duplex outlet on either generator. Then the EMS will be happy, and power up properly.
A really careful, safety first, slightly paranoid generator user like me would also connect the generator's frame ground lug (usually a copper-colored clamp or bolt with a nut on it) to either a driven into the earth ground rod, or tie a suitable jumper wire with an appropriate clamp to a well grounded metallic water system pipe for safety...
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Rich, KE4GNK/AE, Overkill Engineering Dept.
'The Silver HamShack' ('07 International 22FB CCD 75th Anniversary)
Multiple Yaesu Ham Radios inside and many antennae sprouting from roof, ProPride hitch, Prodigy P2 controller.
2012 shortbed CrewMax 4x4 Toyota Tacoma TV with more antennae on it.