Well, there is no reason to panic yet because you can mitigate the risk caused by your shower water if you deploy one of the best shower filters featured here.
The main reason why Chlorine is more toxic in your bathing water than it does in the water you drink has to do with the fact that in the shower, it is re-vaporized.
Once this happens, you inhale it into the lungs where is taken straight to the bloodstream. Researchers have indicated that the amount of exposure to this type of Chlorine in just one bath is equal to the exposure you would get from all the water you drink in a whole day.
A number of brands have been at work designing the right shower filter to neutralize the risk caused by Chlorine and other elements in your bathing water. Not all filters are the same. Some of them are more effective than others.