The reason they say rain water is the best is because it is the purest...percentage wise, without out buying some high tech filtered natural spring water .
Tap water is just fine. But pay close attention to what the P.H. level of your tanning solutions are suppose to be. Tap water in some areas cause your tanning solutions to need more adjustment then others. You will almost never find water that mixes to the perfect P.H. level once all your chemicals are added.
For example I use tap water in my shop and I always have to raise the P.H. level of my final solution even after carefull precision weighing of the chemicals.
It's easy to do. Just add small amounts of acid if it's too high, and small amounts of baking soda if it's too low.
Always dissolve your baking soda in a cup of water before adding it to your solutions. Same goes if your using a powdered acid. Liquid acids can be added straight from the bottle.
While were on the subject of water. If you use tap water, or even well water, and you KNOW it has high iron counts in it, it may be a good idea to get your water elsewhere. High iron in the water will dis-color the fur or hair.