Just my opinion, Mima, it makes no difference to the plant. You should drink your lovely filtered water, and water the plants with the tap water. You can let it sit in a watering can for a few hours if you want the chlorine to blow off, but I honestly don't think it makes any difference to the plant. Here's why:
I have 3 kinds of water, rainwater, tap water and well water. Orchids are supposed to be very sensitive to what type of water you give them because they get nutrients from the air and from water that lands on the leaves. I've watered my orchids religiously with rainwater (as long as I have some) but when we put in our well, the whole outside irrigation system was put onto the well water. It is untreated and has a pH of around 8.2 i.e. alkaline. I was so careful not to use the well water on my orchids, until I had to go away for 3 weeks and put them on a timer using the well water to mist them daily. The orchids looked fantastic when I got back, and I've left them on the auto system with well water misting ever since. As long as I rinse them with rainwater (or it rains) once a week or so they don't get white crusty stuff on the leaves and are very happy. The fact that they do get the white crusty stuff if I don't rinse them tells me they are filtering the water themselves.
As far as the chlorinated water (tap water) a friend of mine had two of his orchids blow into his swimming pool and they were underwater for nearly a full day. He says he was amazed that nothing happened at all, the plants were fine.
Also whenever you need to treat plants with something for bugs or other disease, you're spraying them with water that has a lot of "stuff" in it whether it's soap, or baking soda or some chemical . . and the plants handle it just fine.
