Demineralized may be cheaper than distilled and should be sufficient. If you have a dehumidifier or air conditioner, its condensation is usually good enough.
What can happen has not yet happened to me when I used my well water, which is quite hard. Hard water is good for the heart, so I do not want a water softener, but it would be nice for the washing machine. OTH, most detergents now have chelating agents to prevent soap scum.
There is no arguing with worry warts. I have them in my family. They think I'm just sloppy and will poison them all. There are times when I think "If only it were so."