It is interesting to hear everyone's experience on this question.
I use our incredibly hard tap water for all my potted plants (almost all succulents) except the baby seedlings and the plants in unglazed clay pots. Those get purified (reverse osmosis plus) drinking water.
I see no problem with hard water for any of my full-grown plants (the problem with the unglazed clay pots has to do with the salt buildup on the container after evaporation). I flush every container when I water. Maybe 1/4 the volume required to wet the soil passes through at the bottom. No special ultra-pure water is required to flush if you're regular about it. Alternatively, you can leave your house plant out in the rain every once in a while to let nature do the flushing slow and proper.
Our tap water varies widely in color and hardness from day to day (word to the wise). It's typically quite high in general hardness (GH) and carbonate hardness (KH), with a pH above 9. The main issue with hard water (if your tap water comes out of the ground like ours does) likely has more to do with its pH than its mineral content, if you flush in the manner I have described. The harder the water, the more dissolved carbonate, and the higher the pH. As a general rule. These things can all be measured with aquarium kits. Roots tend to function best at a pH at or slightly below neutral, where most nutrients are available. Around the pH of ordinary unpolluted rain water.
So I compensate for the hardness of the tap water I use for almost all my plants by acidifying it first. I use a product for planted aquaria (bisulfate) to adjust the pH to near 6. You can use various other things too. That's even more salt into the water, but salt of the right kind, and my plants definitely appreciate the extra effort.
