I don't think there is anything harm in tap water. I use tap for all my T's and see no ill effects that would cause any concern. I don't think there are health issues since the tap is treated and cleaned so much. One or the other will have no effect on the molt process to the molt cycles.
how much chlorine is there in the water in the wild?
Depending if you live in a city or not...I used mostly tap water for the first year and a half or so of keeping my inverts...noticed no ill effects. But lately the city I live in seems to have been upping the chlorine level in the water (can taste it more) so I decided for less than a dollar a gallon I could "splurge" and buy distilled water
I doubt it's going to hurt them...but a gallon of distilled water goes a long way
I use tap water. The hard water stains are the only problem. I fill empty water bottles with tap water, and leave them uncapped for a day or two, the chlorine evaporates off. (I do this with drinking water in the summer, too)
Mine get bottled water. My tap water is so horrible I won't drink it, I won't give it to my cat, and I won't even use it to make coffee. It's really hard water with rust and god knows what else in it. It comes out of the faucet sort of orangey with stuff floating in it. EEEWWW!. So only the good stuff for my pets.