It looks like some people are saying it is not. The big challenge is to find water that is free of all organisms. This eliminates bottled water which may come from virtually any source. Even lab purified water is not perfectly clean under a microscope.
No, the only problem with organisms is if they are visible organisms - visible to the naked eye.
There was a problem at one time with something called copepods - or something like that. These little crustacean type things and you could see them with the naked eye. Kosher or not, it looked really disgusting.
Personally, I would think turning the water faucet on Shabbat is a bigger ovoda because it usually runs an electric meter.
I don't think any of the deciders of Jewish law ever considered the faucet use as a potential problem in Jewish law, but I'm not an expert there.
Opening a running fridge or apartment with an air conditioner causes the compressors to work harder. The big question is where do you draw the line? Here is the link to the article.
However, I do know that Rav Shlomo Zalman Auerbach wrote a 30-page teshuva (halachic responsa) about opening the refridgerator on Shabbat, where in the end he permits it. My rabbi in yeshiva told me about this teshuva which he himself had learned. (I think he said 30 pages. It was substantial, I do remember that!) These things are not decided on a whim. But when you start seeing floaters in your water... that's kind of a no-brainer