I have a whole house filtration system, but only because I can't stand the smell of chlorine in the public water system. All my cats drank tap water before I had the system installed about 4 years ago with no ill effect.
Giardia will get both people and animals sick. Most public water suppliers have to keep a level of purity in their systems, which includes the removal of Giardia (it is present in all rivers and lakes in the U.S.). It may be that the levels are so low that people don't get sick but cats, which are more sensitive, can get sick.
When my friend from Denver adopted Jake and Elwood last month, they both came down with Giardia once they moved to Denver. Their vet claims that most cats that he treats for Giardia are those that moved to Denver from other parts of the country. His theory is that there are Giardia strains everywhere, and most cats will develop a tolerance to them in their area. When moved, the new strains will cause them problems for a bit. Jake and Elwood were treated and have recovered quite nicely.
During the blackout, it was so hot in my house that I went to a convenience store and bought a bag of ice cubes for Socks and Skipper, and I put them in a bowl and just let them melt so that they would have really cold water. Socks really liked to put her feet in and to crunch the ice in her mouth. I hope that wouldn't hurt her teeth?
We have one of those coolers/cisterns for Spring Water, that is what we and the cats all drink. I don't let them drink from the tap (although they do try and sneak in there when I'm not looking!).
I have a Pur filter on my faucet. . . . the cats get the filtered water
I recently tried using a special cat dish with a built in filter & pump (like a fountain). My vet encouraged it to get George to drink more water for his urinary tract problems.
He really didn't care for it all that much. . . . preferred the big bowl. . . . and it was a pain to keep clean. It's packed away.
Hubby got a filtration system installed in the house just for the kitties. It's true that the strains of bacteria change region to region. This is why you will get sick drinking the water in Mexico, but the people there don't.
I drink tap water, and so does Luna. I have a Brita water filter, and I do drink from that occasionally, but it's so much easier just to go the the faucet, LOL. I usually only use that during meals, so I can pour more water without having to get up.