Jim, FrankenMauser, yes, spring or well water will have some minerals in it, and not all is hard water, but it's the same water that was used with Herter's bluing back when it was still made by Herter's. If I remember correctly, distilled water wasn't even mentioned back then (See the Brownell's Kinks books).
Myself, and another Gunsmith, (where I apprenticed), used well water in both hot water bluing, (Herter's and Dicropan), and caustic bluing, (Oxynate 7), and we didn't have a problem, before 1987. That was when I was still in Ky., and had soft well water. (I'm not sure what the water was at McCarty's). Here, all that's available is city water, and you have to use something else for hot water bluing.
I used to use Lesage spring water, for hot water bluing, that was actually real spring water, and bottled just across the river in WV. They went out of business, (a law passed making them chlorinate it), and now I have to use distilled. I may try the purified water that they have available, as it is supposed to be filtered, however, I don't know if there's any chlorine or fluorine in it. If there is, those two and acid don't play well together.
One thing I noticed, though it is about caustic bluing, is that on the AGI video about it, Gene Shuey uses tap water for the rinse tanks. This setup drags that water into the bluing. I think he states that he uses the same water to control the caustic bath, too. He doesn't say what his water supply is, whether well or city. Of course, I do the same, and have never had a problem, and it is city tap water. Then again, this is a totally different chemical process, when compared to an acid based bluing.