Plants in media-based systems can tolerate slight fluctuations in pH better since the media acts as a bit of a buffer. For more information about the specific pH plants desire, I would recommend consulting books that feature profiles of perennial and annual plants. Tap water frequently has elements, such as chlorine, in concentrations that can be damaging to plants. The same applies for well water. However, this is not always the case.
Water quality varies from area to area.
Also, plants have varying levels of tolerance for certain minerals. Many gardeners never have any problems using tap water. The only way to be sure would be to have a water quality analysis made. However, these are expensive and unrealistic for most gardeners. You could just try using your water source as a test to see how it effects the plants.