Two questions:
Is the difference between people and animals in this regard based on differences in levels of fastidiousness, or differences in physiology? IOW, are animals as unhygienic as people would be if they didn’t use TP, or are their bodies constructed differently (or their excretions different etc.)?
What do (or did) primitive people do in this regard?
Off the top of my head, not many animals have buttocks. Certainly quadrupeds have just sort of a basic hinge, to steal a description from British T.V., so it may be easier to clean. And I’m sure you’ve seen what dogs and cats have to do to clean themselves, so fastidiousness goes right out the door.
I could check Wikipedia for the history of toilet hygiene for you, but the basic WAG would be, that prior to mass production of toilet paper, people just washed – with a rag, a sponge, their bare hand, leaves, etc. The sears catalog, was anecdotally famous, as a source of paper for wiping, and I’d also heard corn cobs were used – just “scrubby” enough, if not particularly absorbent.
This is somewhat tagential but I thought I would mention that toilet paper is not used the same way around the world. I have been to Egypt several times and in that country as well as much else of that part of the world, it is preferred to used water to clean afterwards. Toilet paper is generally provided but I figure it is more for drying off. Every bathroom I have been in, whether in a hotel, public bathroom, or private home, either has a bidet, or the toilet has a hose next to it (with a handle on the end to control the water, just like what you see in a lot of American kitchen sinks), or a tube right in the toilet that kind of makes it double as a bidet. IME this is a much better solution than toilet paper.
Been to the ME myself and agree that water is much better for cleaning up. I have a bidet in my home in fact, but unless your clothing style allows you to “drip dry”, you still need TP or something with which to dry off.
I’ve never been sure how these are supposed to work. How far up am I supposed to insert the hose?
They wisely avoided over/under arguments because it always lead to someone getting clubbed over the head.
I am surprised with Americans and their hygiene how bidets have not caught on.
All the way up Route 7 until you get to the Beltway.
It’s because they are thrown off by the French name. If they called it “ass washer” sales would skyrocket. 
Ever see the back end of a cow? They’re filthy. Even a human without toilet paper will usually be cleaner than a cow. And without human intervention, sheep tend to get it caked in their wool. It’s not that animals are inherently cleaner; it’s just that they don’t care.
Well, now, to be fair, domesticated sheep have been bred for wool production that you would not see in a wild animal. Wild species of sheep don’t go around with shit caked in their wool, or at least, not that much…
As far as the OPs second question: primitive people didn’t (and don’t!) have white sofas that they sit on. This cuts down drastically on the need to maintain a pristine backside.
Man, given what some people eat nowadays, I can see some cases of lethal diaper rash, or maybe a true flaming asshole.
Cross culturally, is there any difference with differing postures? Like (someone better traveled than I can approach this easily I bet), do squat-style toilets allow for a ‘cleaner break’ on average?
Isn’t diet a large part of the problem? As in, if you ate less x and more y, your poop would be more solid and less likely to leave your bunghole in need of a post-defecation cleaning.
A diet high in fruits, vegetable and whole grains produces soft poop. Meat and cheese produces hard poop.
I have read that they do, and also that the fiber rich diets of many peoples around the world also helps.
It would seem to me that the fiber-rich diets would make for messier poop, and hard meat/cheese poop producing the “cleaner break”.
You do realize that the most efficient use of toilet paper only requires one square. It sure makes a roll last a very long time.
Whut? You weren’t taught that?