One of my pet peeves about restrooms is that so many of them require you to pull a handle on the exit door. So even if you wash YOUR hands, you can still get infected by someone who didn't wash before you.
It may seem anal (no pun intended), but I've been known to use a paper towel to open bathroom doors.
Or I use my sleeve, or part of my top / jacket.
Or sometimes my shirt or sweater is long enough to use on the handle. I try not to touch handrails with my hands, but just rest my elbow a little in case I lose my balance. But even with constant hand washing I was sick on New Year's Eve and New Year's day.