For cacti in general, I use rainwater, just collected in a water butt, and not filtered or treated in any way. My tapwater is quite hard, as we live in a limestone area.
I know that many Mammillarias come from places where the underlying rock/soil ha slots of limestone in it. So in theory it shouldn't matter. But using hard water also creates white deposits where the water evaporates, so can leave unsightly marks on the plants, to the extent that in some old plants there's a really white ring around the neck of the plant - which looks bad, but perhaps doesn't harm.
I use about 40 gallons a time when I water the greenhouse, which isn't a huge cost, maybe only a few pounds, but if I can use natural resources, then I will.
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Chris43, moderator