The difference, as I see it, is that the switch arcs circuit conductor to circuit conductor, and is a series arc; but the ignitor arcs to the EGC.Not any more than a simple toggle switch would, IMPO.
Bad design and I would take that gas range off the arc fault even if there is no code violation. You may be sorry later. I would be curious to know if the igniter would cause a problem on the AFCI. .
You may also ask the inspector if by "AHJ" he means county/city code or personal unction. If he says city code, then you should get a reference. If not, you'll know he's blowin' smoke.
Are all the new gas ranges equipped with a regulator that is operated electronically? I have an old one where the gas could be turned on without power, but my new one won't flow without power.
Perhaps the inspector is my age (translation - "past my sell-by date"):grin: and still remembers gas water heaters without electronic igniters. You had to use a match, and you had to turn the valve in a particular pattern, or it wouldn't ignite the pilot light. If that pilot light were to go out, a small flow of gas could enter the room.
either way the gas regulator is Normally Closed, not open... Otherwise every time the power is off the valve would be open:grin: