I can chime in as I recently moved into a new house with a whole house water softner already installed. To add to the difficulty level, I also do not have a heated water supply that bypasses the water softener.
Basically what I did was I tested an outside water spout, one that wasn't heated, and wasn't on the softner. I then tested the water from the inside tap that was treated by the softner. I then compared the two results and found that in my case, the only reading that was affected by the softner was my Gh reading.
I have 4 tanks in my home with fish from White Could Mt Minnows, Convicts, Jack Dempseys, and Oscars. All of thes fish require a varied level of Gh. To combat the softness issue, I use Cichlid Lake Salts in all of my tanks to varied degrees. It took me two weeks to discover the correct amount of Salts to add to each tank during water changes to obtain my desired level of Gh.
The only problem I've come accross with my water softner is simply the Gh level, which was easy to combat. Currently, the only "chemicals" I have to add to my water during water changes is Prime and Cichlid Lake Salts. Depending on what fish you keep and what your actual Gh reading is from the softner, you may or may not have to adjust.
You may find in your situation that you have a heated water source in your home that is NOT on the water softner. If thats the case, then I would use THAT water source. Either way you go, just make sure to test the water and also treat for Chlorine and Chloramine as the water softner will not eliminate those.