I do turn it off before fueling up (assuming I remember—occasionally I do forget).
Most states (maybe all) legally require that all open flames be extinguished before pumping gas. The fridge running on LP has an open flame—as does the water heater, furnace, and stove pilot light. Turning all of these off is a good idea, besides being a legal requirement.
Even with some electric ignition system, where there is no pilot flame continuously burning, the igniters can come on at any point and make sparks or start the flame. Hence, one should turn off the appliances, not just shut off the gas valve, so that the igniters don't repeatedly make sparks and try to ignite the propane that is not there (and, if one is quite unlucky, ignite the gasoline vapors that are there).
That said, the chances of causing a fiery inferno are slim.