Although I am a good little audiophile and would never think of using anything other than distilled water in my RCM solutions or alone to rinse, I do have to wonder how "minerals" in tap water could possibly do any harm, if you then vacuum dry and maybe even if you air dry the washed LPs. We are talking about very low concentrations of metals in ionic form, in solution in water. It's not as if those ions are going to disturb tracking or groove contours. And by the way, distilled water will still have metallic ions in it, as distillation does not remove them.
And yet, when I had access to water from my lab at NIH (before I retired), which was both distilled and deionized, I used that, but still I am doubtful of the value. As to the rest of the story, read previous lengthy and detailed threads here and read the book by Antinn.