Rain water, demineralized/distilled water is and always has been the prefered choice of mankind and animals if found in puddles or dew off leaves and grass!
Yes I do remineralize some of my DW put over half is taken straight and have been doing so for well over a year now!
No one drinks water in a vacuum if one is not healthy and does not recieve the balanced nutrients which include acidic elements in balance with alkaline,remember it takes both, no water will help them ! Drinking any water one has to get it through copper steel or plastic pipe ,but in distilled water the amount of any metals including copper ,which by the way is an essential trace element, is measured at below the safety levels of consumption, so being afraid of metal distillers is a myth also!
If one researches those who support DW as a healing agent you will find people from Bragg to Reams with people like Fuhrman and many others who supports its use!
Use what you will ,but its too bad you will not be able to take advantage of DW high energy highly absorbable and highly nutrient transferable form of natures purist liquid!
A caveat to you though, or anyone drinking tap water or even filtered tap water is to take Grz advice also and renutrify this highly over Alkaline Water and buffer its hardeness with some form of a mild food acid like pure lemon juice or apple cider vinegar ro help neutralize and make it more bioavailable!
Tap water presents a variety of inorganic minerals which our body has difficulty absorbing. Their presence is suspect in a wide array of degenerative diseases, such as hardening of the arteries, arthritis, kidney stones, gall stones, glaucoma, cataracts, hearing loss, emphysema, diabetes, and obesity. The minerals available, especially in "hard" tapwater, are poorly absorbed, or rejected by cellular tissue sites, and, if not evacuated, their presence may cause arterial obstruction, and
internal damage.(Dennison 1993, Muehling 1994, Banik 1989)