Surprising what you can find when you look for it. There is specific research on aerobic septic systems that suggest no impact from discharge of water softener brine directly to the septic system. From the following article:
http://www.uwsp.edu/cnr/gndwater/privatewells/Water%20Softener%20Use%20Raises%20Questions%20for%20System%20Owners.htm
quote: ***Researchers from NSF found that brine wastes had no negative effects on the bacterial population living in the aerobic treatment tank, even when the system was loaded with twice the normal amount of brine. The tests determined that water softener wastes actually help with treatment processes. WQA’s final report states that the wastewater has “a beneficial influence on a septic tank system by stimulating biological action in the septic tank and caused no operational problems in the typical anaerobic or the new aerobic septic tanks.” In other words, the researchers in this study found that microorganisms living and working in a home aerobic treatment system are not harmed by water softener salts.***