Is Liquid Plumr or Drano safe to use with a septic system?
TLDR;

As a one-off use, Drano® is fine provided you aren't cleaning your floor or doing a couple loads of whites on the same day.

What independent studies say:

According to a 2004 paper by Cornell researchers titled "Household Chemicals and your septic system", despite the assertions of the corporations making Drano® and Liquid-Plumr®, these products can indeed destroy the beneficial bacteria in your tank.  If used in excess, or in combination with other cleaner such as bleach you may encounter problems.

Further, the 1987 study preformed by Mark Gross for the Arkansas water resource title "Assessment of the Effects of Household Chemicals
Upon Individual Septic Tank Performances" claims that for a 1,000-gallon septic tank, the maximum allowable maximum daily dosage of common cleaners is as follows:


Liquid hypochlorite bleach: 1.3 gallons 
Pine cleaner: 2.5 gallons
Crystal drain cleaner: 0.65 ounces


Research Notes:

Many plumbers claim that one should worry about the impact of what ever it is that caused your drain in the first place (fats, sanitary napkins, large solids, washing machine lint), than the use of the drain cleaner it self. For this reason, it is preferable to snake your drain rather than clear it with a Drano®.