Grey water is perfectly reusable in certain ways. There are known standards and known practices that allow the use of grey water in a way that is safe. By using grey water you lessen water use, and extend the water supply so that more people can drink. Nature reuses water endlessly but somehow we humans don't seem to have caught on to this pattern, and instead our supposedly advanced modern society throws away massive quantities of water causing us to overly stretch the water supply available to us.
Grey water is the reuse of water used in showers, dishwashing, clothes washing, flushed down the toilet, etc. There is obviously a concern about spreading disease through grey water, and that means grey water must be carefully treated and used for the right things.
Being Water has developed a series of products that properly filter and enable reuse of grey water. Their systems meet the safety standards of many places in the U.S. Their systems plug into household plumbing and it has the overall shape and look of a hot water heater.