I think there is a product you can get that will help keep the water cleaner and less effect of the softner. I know when I lived in Florida we had a softner. My parent's softner was a lot softer of water than at my own home there. The water smelled like sulfer at my parents, so I guess that is why they had to have it softer.
Water can also change the color of ones hair too. NOt much - more like a hue. If you have rusty water it can cause a slight red highlights to your hair and if too much chlorine can color your hair a light greenish color. The water I have now is Spring water from our well and at time we get gold dust in it. Not enough to filter and save - can't get rich off it. Oh well!
And I am not sure what floride can do in water. I never thought of that one before. They say there is not much in it - city water - and depends on the city, but I know when I lived in my last house during certain times of the month I could smell chlorine a little. We ended up getting filters on our facets. They always got filled with white stuff and had to empty them or change the filters.