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Like they said if its adding sodium that can be fine or good for many fish however some aquarium inhabitants are sensitive to salts. Catfish or other fish without scales, invertebrates, and plants don't tend to be ok with it but I couldn't tell you how much would have to be in your water to harm any of them. If you keep anything like that I'd personally look into it a bit further.
I’ve never had a water softening system, but my understanding is that they add sodium or potassium to the water as they exchange out the hardness. The sodium/potassium is bad for freshwater fish, unfortunately. I can’t find any web references that I trust on this, however. Maybe ask Culligan about what is added to your water by the system?
It is fine for most freshwater fish, in fact, adding a little salt (sodium chloride) at a teaspoon per gallon is considered beneficial and for killies it is essential. The only ones it might not be good for is for ones that live in very soft water, but that is only if you want to breed them, otherwise it is fine.
That is exactly what I have. I use 50/50 culligan/ RO water but they are similar enough that I wouldn't hesitate to use straight culligan water in a pinch.