Propane cylinder valved in...fridge in 'auto' so it swaps to gas when I disconnect AC Power. Fridge has been ON for over 7yrs. I don't turn it off when fueling up.
30+ years of operating boilers I am comfortable with the operation of having propane on.....even when I am refueling for a lot of reasons.
Lot of debate about pros/cons......do what you are comfortable with.