Being female - and using female public toilets - I am always so shocked at how many women DO NOT wash their hands! They just walk out ... so gross!
Maybe, like me, they wait until they are outside and use hand sanitiser. Picked up this habit while travelling in Asia.
Think about it. You turn on the tap with your germy hand, wash your hands, then with your nice clean hands you turn off the germy tap! Then open the door with it's questionable handle.
Exception is more modern facilities that do not involve tap or door handles.
Marg