Running your propane Refrigerators while fueling?

If you are old enough to remember when smoking was very popular, filling your car. lawn mower, 5 gallon fuel carboy, chain saw etc. With a cigarette dangling from you mouth was common.

Was it smart? probably not.
Was it safe? probably not.
Did it cause numerous explosions and gas pump fires? No.
Did anyone care or give it a second thought? Not really.

Turning your propane off certainly cannot hurt but most folk do not feel it is an issue.