Yeah, fluorine is some pretty nasty stuff before it's neutralized by something bonding to it. People have the stereotypical image that fluorides in public health services are dangerous. They're really not. They do that for a reason - it's the reason why your dental bills aren't thousands of dollars monthly and why you aren't dying from tooth infections left and right.
Chlorine is different, it's to sterilize the water, and it's not killing you. It is not in highly toxic concentrations to humans, only to bacteria and other water-borne organisms. You'd die of your nervous system shutting down from waterlogging before you die from chlorine poisoning.