Insurance will not allow the top dangerous breeds which I can't recall all of them but they do include Pit Bulls, Rotweilers, German Shephards, usually breeds that are already protective and often have this behavior encouraged by idiot owners so they have a high reputation of biting.
You should insist on a dog crate. Period. Often dogs who are not used to traveling if left alone in the room will scratch the door anxious for the owner.
And no, you should not allow them to be left in the rooms, but the owners who are not responsible WILL leave them alone, so if you have required a crate for checking in with a dog, at least if they are crated they can't create damage.
And don't think the crate is something bad. Dogs are animals that like a cave so when they are properly brought up the crate gives them a sense of security. Ours used to trot into their crates to take a snooze at home all the time.
There's no way to house a cat without a litter box. They may have small travel ones, but that's something you would have to provide and charge them for. Are you ready to remove and dump them? I would not depend on a pet owner to be responsible enough considering the damage from just people. I'm still working on two pillowcases from this weekend that have what looks like black hair dye on them and don't think the stains will come out.
And don't get me wrong - I am a pet lover, my mother used to show dogs and we traveled with them all over when we lived in Europe where they are more pet friendly. But we were considerate pet owners and trained our pets. We went out to dinner every Sunday in Switzerland with two Russian Wolfhounds to our neighborhood white tableclothrestaurant and popped them under the table. They were good because they never received treats when out to dinner.
When shopping and stopping in a coffee house, now that was different. They always got a cookie from the waitress but knew they had to wait until just before leaving...and they loved to go to the hairdresser with my mother!