As long as there's paper towels you can lather, wash, dry with a clean paper towel, and then use that to turn off the faucet/open the door without touching them. It sounds germophobic, but it really is the best way for us to use public restrooms and protect each others' health.
My understanding (which may be false) is that this can come about from competing design considerations and regulations. Like... It's ideal to be able to push the door open from the inside of the bathroom so you don't have to touch a nasty doorhandle, but you also don't want somebody to be able to put something in front of the door, potentially trapping you in the bathroom (particularly in the event of a fire... Dying in a fire is probably worse than touching a nasty doorhandle), and you also don't want doors to unexpectedly swing open into busy hallways. This drives me nuts too, though.
Eh, there's an easy solution that a lot of places are starting to use. A foot pull. Probably costs $5-10. No real excuse for any place not installing these.
Don't think you need it that much. You're going to wash your hands after. There's a small chance you could contract something before using the bathroom from it, unsure on the likelihood of that transmission.