Regular toilet bowl cleaner won't hurt your septic tank (it's the same acid we have in our stomachs.) If you can find The Works, which is a cheap brand, it's about the strongest on the market and it works best in our hard water. The rings are mostly calcium, after all, so the acid will dissolve them.
Another possibility: if you have flat soda around, you can pour it into the toilet bowl and leave it overnight. Denture cleaner tablets also work, once again best if they're left overnight. I'd only do one toilet at a time, for obvious reasons