Softened water has had a large proportion of the iron and other minerals removed and replaced with sodium, this can play some games with your pH but honestly I've never had a problem. You can actually use purified chlorine gas diffusion to turn the sodium back into salt in the water then treat the water for chlorine if you feel like spending a couple thousand dollars just to get rid of the sodium. I'd not worry about it. Check your tap water's pH without aquarium treatment, if its under 7.4 and above 6.8 it's fine. If its over 8.0 then its not being softened very well.
Don't drink softened water or boil it down for cooking, its primarily done for clothes washing, showering and to keep house pipes clean of hard deposits.
(Ion exchange resin, what is used in softeners, is treated with salt brine. The resin will pull iron and iron-like materials out of the water. When the brine is washed over it the iron is displaced by sodium and then iron chloride, a green mineral, is rinsed out in the waste water. Because the sodium is released into the "for use" water it literally replaces whatever ppm the iron of the source water was with ppm of sodium in the water.)
API sells little $5.00 pouches of ion exchange resin which you can stick in your tank's filter or - as I prefer - stick in a filter and run in the replacement water bucket. These pouches are regenerated using a container of water mixed with aquarium salt. The longer you process the water the softer it gets, the two I've gotten seem to be limited to about pH 6.4 down at about 10ppm hardness (half drop in test kit)