Tap water for mushrooms

If you live in an area where it is safe to drink tap water, it’s totally fine to use tap water for your mushrooms. Many municipalities add chlorine or chlorine compounds to drinking water to kill microbes and prevent disease. These compounds may inhibit mushroom growth to some degree, but the concentration in drinking water is low enough that we aren't concerned about it.
If you'd like to avoid using chlorinated water, you can leave your water out and exposed to air for 24 hours. This allows the chlorine to evaporate. If you use a filter for your water, you can certainly give your fungi filtered water as well!