you need A/C, you definitely will need a generator. Obviously, all else on the A/S is intended to / designed to / can / does run on propane and 12 volt
. You can get more of that 12 volt
power e.g. for lights, furnace blower motor, refrigerator circuit board, etc. from solar panels - or a generator.
But if you need A/C, (absent a LARGE solar array) only a generator or grid connection will do that ... then it's up to you what sort you get and what fuel it uses. You can get gasoline, you can get diesel, you can get propane, you can get natural gas. Each has its place. But all these fuels are flammable, all have hot exhaust gases - so not clear to my why you wouldn't be able to use propane in a place where you can burn gasoline.
BTW, there are available for camping, off-grid, emergency, and other similar use, refrigerators that run on kerosene / fuel oil, as well as pressurizaed lights, kerosene stoves, etc.