Cats dislike standing water, fresh or not, cold or room temp. In fact, most cats who do not have access to running water will be dehydrated all the time. This usually isn’t a big problem for them because they have awesome kidneys, but it is why most cats’ pee smells strongly of ammonia – it’s too concentrated, because the cat isn’t getting enough water. However, this can be a big problem for male cats, who are prone to urinary troubles because of their extremely long and narrow urethra. I’ve known two perfectly healthy male cats who died from FLUTD, and my own buddy almost bit it a few years ago, which is when I learned all this. A cat fountain is a cheap and simple way to get your cat to hydrate himself more, and is much safer than letting him drink out of the toilet. I own the model I linked to, and it’s quiet, easy to clean, and has lasted three years so far.
The issue with the toilet is actually not so much the bacteria from waste – as mentioned above, we clean this out – but is that the chemicals from cleaning the toilet are bad to drink (unless, I’d imagine, you clean your toilet with bleach-free organic stuff, I guess). Keep the lid down, folks.