I wash them so my hands don't stink, so they don't become sticky, basic hygiene really, so anytime I touch something that changes the texture/feel/nature of my hands.
Also despite your body being host to millions of bacteria, those live in harmony in your normal healthy body. The same can not be said for foreign bacteria, so you should definitely wash after poop, touching animals that aren't your pets, in any lab environment, or the fucking public toilet, that place is a shithole.
Honestly I judge people who don't wash in a public toilet, heck even a one second rinse would alleviate my disgust.