Dear mammalicious,
The reason why it is not recommended for babies to drink water from a softened water tap, is that the chemicals used contain a high amount of sodium, which is difficult for baby to digest, and can lead to kidney damage.
However, if you give your baby bottled water, they will be missing flouride, as well as other trace elements. (The debate over mineral vs distilled water has been done here before, la)
Apparently, you shouldn't even use softened water in steam sterilisers.....(well, according to my mother-in-law.....)
Hope this helps,
HappyV