Actually the chlorine thing is a bit overblown for sauerkraut. Most tap water in the US has around 0.5-4 ppm chlorine, which is really low. The lactobacillus bacteria that ferment cabbage can totally handle that. I've made like 20 batches with straight tap water and never had a problem. The bigger issue is if you have a well with super high mineral content or something, but standard municipal water is fine. Letting it sit out overnight does help with the taste though, makes it less pool-watery.
Yeah, the "use tap water for sauerkraut" thing is a real debate. I read that the chlorine in most tap water can kill the good bacteria you need for fermentation. Some people say to just let a jug of water sit out overnight so the chlorine evaporates.