Topic has been beat to death
Other than tunnels/bridges/ferries where it is REQUIRED to be OFF I travel with propane valved in service and Fridge ON....even have traveled with Furnace ON
Propane System has numerous safety features and propane appliances have safety features that make operating propane while in transit safe.
Safe enough that IF I couldn't use propane while in transit I would NOT use it while asleep.
Know and understand the varies safety features built into system.
Then decide for yourself.
Doesn't matter what others do.........