Comment by thePhytochemist

The chlorine you are tasting in your water is an active, reacting compound. It has to be because it literally reacts with cells to kill them and keep the water (relatively) free from living organisms. It's great as a cheap way to keep living things out of the water but at the end of the pipe it should be removed - a simple Brita filter is fine.

Flouride added is in a chemical state that makes it stable, like the chlorine in table salt. It will stay at the same concentration as it travels in the pipe.

I remember this from a water chemistry course at university.