Everything is relative in this question. Is it "safe" to drive with the propane and fridge on? More or less, "Sure", if you aren't involved in an accident which ruptures the propane line, or if you don't refuel the truck with the propane and fridge "on". Is it "safer" to have the propane and the fridge "off" while traveling? Also, "Sure!"
All that being said, if you think the chances of you having an accident which involves the propane line or tank is 1:million, and the chance of an accident which would rupture the propane tank anyway is 1:10 million, then maybe it isn't a big deal. Just remember to fuel your truck without the rig attached. We almost never travel more than one tank of fuel will take us in a travel day. We usually refuel after setting up in the RV park, or before hitching up in the morning. Alternatively, shut off the fridge and propane before pulling up to the pumps.
Just MHO.
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