Our pets are most assuredly not allowed on the furniture under any circumstances! That would be disgusting. Why spend all that money on an aquarium for them if we’re just going to give them the run of the house?
We always allowed them on the dining room table, because it has a tablecloth on it. One of the best tricks was that Fluffy would jump up on the table and run around the top of it, while the dog would run around the bottom, barking at her. She was such a snot-she used to sit in front of Lassie’s crate when the latter was a puppy and the dog would bark and bark and she’d just sit there, smug.
Of course, they aren’t allowed up there while we’re eating dinner, since there’s no room. But if I’m eating lunch, and the cat is sitting on the table, no big deal. Hell, I’d even let them have a taste of what I’m eating.
Three cats (Tasha, Cara & Tee), two rats (Milo & Rodney) and a Mastiff (Gracie) in our house. The rats are only allowed out of their cage under strict supervision, and then usually confined to our daughter’s bedroom, but they are allowed on her furniture.
Gracie is not allowed on furniture, for no other reason than she already outweighs my daughter and is fast overtaking me, and there’s just not that damn much room on the sofa. Eventually, she’ll probably sleep in our bedroom on a big cushy dogbed, but she’s still crated at night at this point.
The cats are a whole 'nother story. They go wherever they want, whenever they want. I’ve never seen either of the females on tables or countertops, but occasionally Tee will first make sure I am looking, then hop gleefully onto the countertop so he can get chased off. Cara sleeps on top of the rat cage, which doesn’t seem to bother the rats. Tasha and Tee sleep on me - Tasha on my ass, Tee on the backs of my knees or across my neck.
Animals are not allowed in the house. They live outside, I live inside.
Both of my cats have the run o’ the house, but they know that under NO circumstances are they allowed on kitchen counters, dining room furniture, or the coffee table. Any other place is fine. I finally finished moving yesterday, and they seem to prefer the hardwood floor, since the A/C vents are there. Boy has it been hot here.
Presley, the overweight Border Collie, is allowed everywhere. We could put a cheeseburger on our coffee table, and he won’t touch it. If it hit’s the floor, it’s his. The Room & Board overstuffed chair has a dented arm from where he rests his snout daily, waiting to defend our home from the ravages of the evil mailman. If my wife is in bed alone, he’s on the bed. When I walk in, he hops off. We got him from the pound, he was a stray. We don’t know his history but he obviously had training at one time. Weird incomplete or just goofy training.
Bitz the Wondermutt can go anywhere in the house she likes except the library, into which she must be invited, and the master bedroom (same deal).
She’s not allowed on the furniture, but that’s okay; she’s never shown any interest in getting on it. Besides, it’s not like everything isn’t already covered in her her hair.
However, being a razor clawed 94 lb. Labrador/Rottweiler who is either hyper or comatose, the longevity of the furniture kind of dictates that her happy butt stay off it.
Speaking of being covered in her hair, I can’t understand how a mutt that comes from two such allegedly low maintenance coat breeds of dog manages to shed such giant fur bunnies all over. She gets brushed at least once a day, usually two to three brushes full of hair, and it’s still all over the house two days after sweeping. She’s healthy as can be and even my vet can’t figure it out.
I wouldn’t trade her for anything though, even if I caught her lying on the couch drinking my best Scotch.
Spunky the Wonder Lhasa goes anywhere in our home that he wishes, except the service hallway and is allowed up on the sofa in the TV room, the ottoman under the desk in my office (we share it when I’m working), the foot of our bed on his “blanket” (really an old, soft towel) and on our laps wherever we are, unless we’re holding the baby. He’s afraid of the baby, anyway. She makes scary noises. 
He’s snow white, so if he had a dirty bum, we’d know instantly, and he’s clean 99.9995% of the time.
He has, on occasion, had instances of having a little something on his fur, but that only happens if he has a stomach problem (usually from being given people food that wasn’t good for him, so it’s not hard to avoid) which causes less than firm feces. That’s easily dealt with by either giving him a bath or simply giving him a wipe with a baby wipe. He likes being rubbed all over with baby wipes, so that’s not a problem.
As for his feet, we keep the fur between his paw pads cut very short, because he hates it long. We use musher’s wax on his paw pads to protect them in the summer, which makes them easy to wipe off, and when it rains and in the winter, he wears boots when he goes outside. Since I eschew shoes and socks at almost all times, his feet are probably a bit cleaner than mine.
The dogs are allowed on any furniture they like.
It’s the kids we keep in the basement. They also sleep in cardboard boxes by the furnace.
But the dogs? Yeah, they have the run of the house. (Lucy, the Jack Russell Terrorist, sleeps under the covers at my feet. It’s easier that way.)
-Rue. (who lets the kids up for playtime at least twice a day)
My cats were allowed everywhere they could get to. Then I got married.
Now the (different batch of cats) cats are not allowed outside (limited exception), on eating/cooking surfaces, garage, utility room, crawl space, attic, or my wife’s desk - everything else is OK.
As for the butt issuse cat’s (I’m not sure about the correct term here but here goes) assholes will kind of push/fold outward when they shit. when they are done that fold is what is outside and never touched the shit.
Also they clean their butt w/ their tung.
My cats were allowed everywhere they could get to. Then I got married.
Now the (different batch of cats) cats are not allowed outside (limited exception), on eating/cooking surfaces, garage, utility room, crawl space, attic, or my wife’s desk - everything else is OK.
As for the butt issuse cat’s (I’m not sure about the correct term here but here goes) assholes will kind of push/fold outward when they shit. when they are done that fold is what is outside and never touched the shit.
Also they clean their butt w/ their tung.
Our cats (Meep the Russian Blue and Tenshi the Singapura) have the run of the house, and this includes furniture and kitchen counters. We rarely eat at home and when we do we wash the counters, so it’s no big deal. They’re both rather strong-willed individuals, so trying to discourage them from being where they want to be isn’t very effective, and they give us so much fun and love that we don’t like to deny them anything reasonable. Besides, I’ve waited a long time to be able to sleep with warm furry cats (spouse had to get allergy treatments before we could get the cats) and consider it one of life’s great pleasures.
The only place they’re not allowed is inside my and the spouse’s office rooms when we’re not home, because Tenshi is an aerialist and there are too many things he could get into in there. Plus the rats used to live in the spouse’s office, but unfortunately they’ve both passed on now so that’s no longer an issue.
It’s the same in our house too. Our four cats also let us sleep on their bed.
With regard to the OP I can understand his concern but I don’t think you can really compare a human against a cat when it comes to not wiping oneself. Unless the cat is having digestive problems in that area, there’s really no residue “undertail” to speak of. With four cats, we are well acquainted with the aroma of feline excreta, and it can be powerful before they cover up the evidence. I imagine if a human being took a dump and then walked around naked, or even cloghed, without wiping the stink would be pretty noticeable. But, I’ve never smelled anything on a cat, unless, as noted above, the cat is physically sick. Catsh** must simply have a different consistency and tend to come out firm and clean (God, I can’t believe I wrote that).