Well, you didn't say what rig you have, but in general only the smallest RV refrigerators run on 12v (because the power requirements are so high in larger units).
The fridge is designed to run on propane while under way, and that's how most of us use it. In the old days they had pilot lights which ran all the time, but now there is a piazzo electric igniter, which is much safer. That being said, most of us turn the fridge to off, while at the gas pump.
Use it as it was designed to be used, and don't worry about it.