Buggerama, the desire to hide one's poo (bury it, flush it away, etc) is probably instinctual. I think most people are concerned about leaving something so personal and gross to be seen by anyone, even their cleaner.
I don't mind cleaning toilets. In fact, I like it. But, I once had a client with a broken toilet and four kids who kept on using it. Once a week, I'd pour a bucket of water in it to flush it and then clean it. (Imagine how gross it was after sitting there like that a week!) I asked her when she'd be getting it fixed and she indicated that it wasn't a priority so I told her I wouldn't clean that toilet any more. I don't mind cleaning toilets - I even put my hand in them and scrub them - but that was just disrespectful (and it was only one of several issues she had that made her not worth keeping as a client.)
If someone forgets to flush the loo, I don't care. And, I would hate to think that someone would NOT hire a cleaner because they stressed too much about trying to make things nice for me. But, I have my limits.
I have a written policy to the effect of:
"Health and Safety: MyCompanyName has a policy of not dealing with deposits of blood, urine, vomit or faeces, human or otherwise. Cleaners cannot remove or dispose of syringes. Cleaners will not empty or clean litter boxes or pick up animal droppings. If a property is found to be infested with vermin that may pose a health hazard to the cleaners, or may infest My Company Name equipment, then work will not be carried out until the situation has been resolved."
When I used to clean holiday cottages, some guests once got drunk and one of them was sick. They left the mess for me to clean. I had to clean it because it was a holiday rental and more guests were due in a few hours and of course someone had to clean it. But, the owner gave me their entire deposit!
If someone's dog has a little accident, no problem. But, if someone just expects me to deal with their biohazards because I'm "just a cleaner" then they can find somebody else.