Does hard tap water cause problems for my plants?

Measure your tap water first. If the EC is already high, count that as part of your feed and cut back on Cal-Mag, because you are getting some of it for free. The bigger headache is usually the bicarbonate: it makes pH drift upward after you correct it, so expect to need more pH-down and to re-check after 15 minutes.

Very hard water is often easier to handle by cutting it with reverse osmosis water, then building the feed back up. Get a decent pH/EC meter and a pH-down such as GEN200 pH-; add it drop by drop, stir and measure again.