RVers are pretty evenly split between driving with propane on and not driving with propane on. Often the discussion gets highly contentious.
The concern is that in the event of a propane leak (hose gets broken in some way) that there’s the potential for a fire/explosion if a spark is involved. The counter to that is regulators generally have a diaphragm in them that if propane is passing too quickly, it automatically closes (you can experience this if you open your propane bottle too quickly).
You may also consider turning off the fridge while filling up at gas stations being that the burner is an open flame. There’s concern it can ignite the gas vapors around the pump if it’s near one.
You have to make a decision on benefit vs. risk for you personally.
I personally drive with it on and don’t turn it off when filling diesel as it’s typically 20′ away from the pumps.