It might depend on what kind of water softener you have.
The newer ones only use minimal salt and can be compared with rain water for salt content.
We have some of the hardest water in the cities up here and it leaves the brown stuff you are talking about.
We have one of those made by Kenitco Water softener. And use it to water and have had no problems with the hosta or any other plants.
Downside of this is the city charges you sewer fees by how much water you use...