It doesn't bother me for drinking, but I've gotten in the habit of keeping an open (loosely covered would probably work too) pitcher of water in the fridge for making coffee, so it sits at least overnight before use, and dissipates some (having already served its purpose.)

Apart from me mixing up chlorine and fluoride, my comment was a bit hyperbolic - of course, there's no Big Filter industrial complex :)

I haven't done a lot of research on how to clean water, but e.g. in Germany, tap water isn't chlorinated and thus has a much more neutral taste. And it's very much regulated to a high standard.