Filtering your drinking water is necessary to avoid fluoride, chlorine, and other toxins. Even if you do have a drinking filter; it's also important to filter the water in your shower.
Many people don't realize that when you take a hot shower, you end up inhaling the fumes from the chlorine. It's also absorbed through the skin, and can kill your beneficial gut bacteria.
Dr, Mercola explains the importance of water filters and discussed whole house systems.