Bathing cats can give them infections if the water gets in their ears. Generally, they clean themselves in a freshly cleaned litter box, what's called a "sand bath" by rolling around. They also clean themselves by licking themselves. They do a very good job, I've been around cats my whole life and none of them smell except perchance the fat ones that cannot lick their butts and sometimes have a bit of a dirty butt.
I'm not sure if you asked the question in regard to disease -- but even indoor cat poop will not carry diseases. Perhaps E. coli or other bacteria already in the cat's gut (and our guts too), but toxoplasmosis is not going to pop up unless it's in the cat food (uncooked pork, etc.) or the cat already has it. It is another common mythology that somehow poop has "disease" in it. It has no more disease than we already possess...
I'm sorry, but is this a joke and I'm just missing it? I find it hard to believe that you are seriously suggesting a cat rolling around in a feces-covered litter box is "cleaning itself".
>freshly cleaned litter box
There is essentially no such thing as this. You would need to completely remove the litter and sanitize the box with bleach _each time your cat poops_. No one does this, they scoop out poop and put the contaminated scoop in a bucket or something. The next time the cat enters the "clean" box it is covered in it's own feces, and your scoop acts as a cross-media reinfection device. Litter boxes are, in practice, perpetually dirty things.
Cats are not "clean" after they lick themselves, if anything this behavior is primarily responsible for the cultivation of a parasite lifecycle that has co-evolved to the cat's gut.
Cats, especially ones who share litter boxes, routinely get covered in potentially parasite-bearing feces via litter boxes and ingest it via grooming. This allows for easy additional spread/cross infection.
"Cats lick themselves, therefore they are clean" is a long-discredited but persistent myth.
