Personally I wouldn't use tap water on a regular basis, but it depends on your water. I use a water filter on my tap which I think is good enough, most of my water is distilled for my MK. For the shower it probably wouldn't be terrible, but I added a filter to my shower head. Screws right in, and is good for your skin too(apparently).
They have solutions you can mix with your water to take out anything that may be harmful to them. I live in AZ and have incredibly hard water so I typically just used bottled water.