Some folks are adamantly against towing with propane on; I never tow with it off since we live in South Texas and travel primarily in the summer, much of it through the desert southwest. When I refuel, I never have the refrigerator panel anywhere near a gas pump; the trailer is way behind my truck in the parking lot. I also use diesel, so I go to the outside diesel islands.
One word of caution if you choose to turn off your propane before fueling...do it away from the pumps and turn your refrigerator off, NOT to AUTO. What would be really dangerous would be for your propane refrigerator to start sparking to self-start near a gas pump!