If the generator is installed properly, there's no need to leave the door open. If you're referring to a door or panel on the generator itself (as opposed to one on the RV to get at the generator), having it open or removed will often lessen the cooling efficiency of the generator by allowing cooling air to escape rather than flow over the hot bits to cool them down.
Many people run the generator while on the road, and it's not really a safety hazard or otherwise a bad idea. You do need to shut it off (along with the main engine) when refueling, of course.
