Is even transporting propane dangerous? Well yes, as well as transporting gasoline, and a bunch of other stuff! I guess it comes down to your definition of dangerous, does that mean every time you leave the house, (the house is dangerous also, home accidents), you are going to be killed? Or does it mean that something has the possibility of happening? Yes, under the right circunstances with the moon aligning with mars, the propane system could develope a leak and explode and burn your RV to the ground. Will it, probably not. Gasoline is just as "dangerous" or more so, but we use it every day, almost 50,000 people are killed every year in auto accidents, do we ban cars? No, we live with the possibilities.
I think the OP was asking if you could damage the fridge by running down the road with it on, as opposed to how safe propane systems are. Most on this site do run the fridge while driving, and someone was kind enough to post info from manufacturers stating it was not going to damage the fridge by running them while driving!