This is a game theory scenario:
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I’m too lazy too lazy to wash my hands or don’t feel it’s necessary. Upon encountering this door I see both handles and decide to follow their instructions and open the door for unwashed hands. My hands are now unspeakably filthy as filthy people following the signs have accumulated a ton of germs on this handle. I get sick.
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I was my hands, follow the signs and use the washed handle. Unbeknownst to me some unwashed game theorists decided that obviously the handle for washed hands would be cleaner so they used it without actually washing their hands first. It’s now also filthy.
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I didn’t wash my hands, I don’t give a fuck about signs, use the one most convenient for me.
Depends what you do next and how much germs or on the handle. Worst case scenario someone shat themselves and tried to clean themselves up and contaminated their hands. Didn’t wash up or didn’t wash enough and left fecal matter on the handle. You then exit the bathroom and go eat a burger or some finger food so as to transfer germs directly to the food entering your system.