The only thing my fingers touch while peeing is my dick. I shower 2 or 3 times a day. Its very clean. Do you think my hands become filthy after touching my dick, as opposed to anything else? My foreskin is probably significantly cleaner than my hands on average.
You should regularly wash your hands to keep them clean. Bathroom is a good checkpoint. But if I just washed them and peed 15 minutes later, theres no value in it.
Germophobes are really silly. If only you saw all the bacteria you interacted with, lol. That part of my body is physically injected into other humans, even!! No one gets sick!
Taking a shit is different. Your colon is full of ecoli and may get on your hands. Urine is sterile until it leaves the body.