This has been debated by many people for quite a while. The short answer is yes, you can, and most people do. Having said that, this can be dangerous in some situations. If you are gassing up and the fridge ignites, the spark could be a hazard. If you were in an accident, an open propane line could be dangerous.
Still, most people do run the fridge on propane while traveling.
If you don't want to, then you can put frozen ice packs in the fridge. These will help keep things cool as long as you don't open the fridge much.
2012 Cruiser Sahara 330SS
2015 F250 Super Duty diesel