People will do what people do.
When I had my TC's, I would fill the diesel (all components and appliances off) a day or two before heading out.
Then at home, I would pre-cool the fridge on shore AC and pre-heat the water heater. When I was ready to travel, I would shut down the water heater for travel as it seems to retain the heat pretty well.
Depending on time of distance travel, I would generally not turn on the fridge while traveling. It seemed to keep stuff cold for a 3-4 hour travel if not opening the fridge door.
Sometimes I would travel with LP fridge going but ALWAYS turned it off before approaching the pumps. The water heater and fridge were right close to the fuel door and for the sake of safety, the extra 20 minutes or so to LP down and then LP up was not too much a price to pay for taking prudent precautions.