Very hard water can be harmful to your plants because of its high pH it creates alkaline soil which in the long term can damage or even kill your plants.
Like most other plants your lawn can only tolerate so much salt, therefore softened water can sometimes be harmful to your grass.
Normal plants cannot tolerate brine from your water softener, but certain salt-resistant plants will thrive when watered with salty water.
Generally, the salt concentration within the backwash is simply too high for your lawn to stay nice and green. However, the solution to pollution is dilution.