Lots and lots of discussions on these forums and no one has ever been able to provide bonified evidence that it is illegal anywhere to run the refrigerator while traveling on the road. There is a lot of folklore about gas stations and explosions, but there again, there was only 1 instance that is known, and somehow, it's become the hysteria all these years. And if I understand the story, it resulted because someone spilled gasoline from the pump hose directly on the camper and fumes ignited.
The audience is about 50/50 on these forums, for or against traveling with the refrigerator running.
Of the 50% for, a small segment state they turn their gas off when fueling at gas stations. (believable or not? that's what they say.)
Bottom line is, do what you feel comfortable with. But when the ice cream in your freezer turns to runny goo and leaks out the doors, I bet you'll either leave the ice cream home, or leave the refrigerator turned on when traveling!
It's your call. Do what makes you feel most comfortable. Some may disagree, but there is no right or wrong here.