We run ours with the door shut occasionally with no problems so far. By the way, if your rig has the TV coming up from behind a fireplace or something else and forget to lower it when you aren't supervising, cats will go down in there. You can guess how I know.
Dick, Joyce, Diego, Picatso and Gustav
2017 3720 RL, and 2013 HC 343RL
Pullrite Hitch, IS, Disk Brakes, 3rd AC, Winegard Traveler, Bathroom door mod, Dometic 320, couch for desk swap, replaced chairs, sun screens, added awnings, etc.