Hydrogen peroxide is H2O2. The over the counter stuff is only 3 to 5% concentration. The septic tank works by anaerobic bacteria (no oxygen bacteria). Peroxide destroys bacteria when the extra oxygen atom breaks off to leave a water molecule and a free oxygen atom which is very reactive (free radical). When this free radical touches a cell wall the reaction can blow a hole in the cell wall destroying the cell. But the concentration of the OTC peroxide is so diluted that there will be no effect on a septic system. I suppose if you dumped a 55 gallon drum in every day you might have a problem.
What concerns me most about septic is all the antibacterial soaps we use. Municipal sewage sludge has routinely been used as fertilizer. But the two trichloro compounds which are used in these products have resulted in zero microbial activity in soils where the sludge is now being applied.