Nothing happens, when C is added to HNO3, which may be present in rain-water at VERY strong dilution.
All the kind of reactions, discussed above may occur, when carbon comes in contact with concentrated acid, but believe me, none of these will occur in a rain-water storage tank.
The same is true for any sulphuric acid or sulphurous acid, which may be in the water in trace amounts. It does not react with the carbon at such strong dilutions.
Of course, there could be bad chemicals in that water (e.g. stuff from the roof, dissolved metal salts from atmospheric dust, etc.), but I would not worry about reactions with the carbon in the filters.