Product recommendations for clearing a drain connected to a septic system?
I stay away from chemical solutions all together.

I have had reasonably good luck with using a drain snare to snag most of the hair in my tub drain.  Every few months, I will shoot one down the drain if I see it getting a little slow.  This will normally clear things up without any further intervention.

When that fails, I usually move towards using a hand crank drain auger.  This will allow you to get further down and (usually) past the trap.  

If that fails, then there is something more serious going on, and pouring a bunch of caustic chemicals down the drain isn't going to help the situation (especially if you need to eventually open up the pipe to inspect further).