Chlorine could affect the plant as noted not fluoride. Water filter, great idea. After a couple hours in an open container the chlorine will dissipate. Actually after bottled water has been opened for three hours or so, starts to develop bacteria at a faster rate. Supposedly most tap water, after the chlorine has dissipated is better than bottled water. This was from a new article several years ago in Ct. Water here is highly chlorinated, you can see the color in a tub. My only problems have been too much moisture, medium, and gnats, not the chlorine.

Big Berkey.. I love mine. I wouldn't drink unfiltered water, or give it to my pets or plants either. The city water here smells like chlorine and who knows what else is in it.
When possible, I also collect rainwater for all my houseplants, or those plants indoors for the winter, figuring that this would be best and most natural for them. I just put a bucket outside, and then it can be stored in plastic gallon containers.