Is it safe to use liquid drano in the drain that my washing machine drains into?

I would say it wouldn't be because often when I wash clothes after I washed greasy work clothes the grease somehow backs up and gets all over my other loads.

is it safe to use liquid drano in the drain that my washing machine drains into?

I am no fan of putting harsh chemicals in your drainage system, especially if you're on a septic tank. You washer drain line clogs up with grease and fiber and the only sure way to clear the drain is to snake it. You may snake the washer drain from one of two places. The washer stand pipe or the washer roof vent. If you go down the vent put out enough cable to reach the base and 20 feet more. \Good luck, Tom