Keep in mind that chloride ions are actually required for photosynthesis, in concentrations even higher than Fe+. It all comes down to the particularities of the running water you have in your location and your growing setup. It's a good idea to analyse or find out about the minerals in your water and its pH. Like hereje pointed out, excess chlorine can be easily evaporated leaving your tap water rest in a bowl for a couple days, if it's present in high concentrations. Most of the problems with tap water have to do with hardness, high pH and high concentrations of dry residue, especially calcium carbonate. A little bit of investigation might result in good news - like knowing the treatment your tap water requires to be used efficiently as irrigation water. This can include pH correction (phosporic acid works great for gardening), micronutrients supplementation, or the need for a light reverse osmosis filter. Measuring EC is also interesting to prevent nutrient burn... different waters need different amounts of fertilizer to get a balanced EC.
Distilled/deionized water can always be useful (germination, rehydration, misting, etc.) but as mentioned before it does not deliver anything to the soil but solvent.
Mandrake