Yes, it is safe to use Liquid-Plumr products if you have a septic system. The ingredients (sodium hydroxide) become highly diluted, degrade rapidly and will not harm the bacteria in your tank.
Septic tanks are really resiliant and what causes the most failures is lack of maintenance and laundry soap. It is amazing that people live in a place 10 years without maintaining a system at all then wonder why a failure occurs. Know where the septic tank is and inspect the surface scum layer and sediment level each year. If surface scum gets more than 5" something is wrong or you need to pump. Problems occur when the surface scum builds up to where it can pass through the baffle to the secondary chamber. That chamber should always be clear of solids. Preventing any buildup of solids in the secondary settling chamber in the tank is key to maintaining the leach field which is where the wastewater is actually disposed. Pump every 3 to 5 years for optimal results and add back cultured anerobic bacteria.