Never. Bacteria is beneficial, especially bacteria from the gastrointestinal tract. You help maintain a diversity of antibodies and thus a robust immune system by avoiding hand washing altogether. And when you do wash them, use only room temperature water.
Reports of sickness at eating establishments have made people irrational on this subject. But it is actually detrimental to your immune system to reduce microbe diversity by vigorous handwashing including before the handling of foodstuffs in the food service industry. The actual cause more often than not of these incidents are not from employees not keeping their hands sterile 24/7 but from spoiled meat such as using long expired meat that was not stored at a low enough temperature to cut costs. Or because of pre-existing food allergies.
The babies most likely to get sick are ones who are kept in a near-sterile environment in the first months of their life - as is common with newborns these days. Their parents will use all sorts of cleaning solvents to wipe out as many micro organisms as possible in their living area and this results in the baby's antibodies being extremely sparse and makes them more likely to get sick.
Henry VIII had his servants obsessively clean his son Edward VI's living areas multiple times a day. He grew up constantly ill and died at the age of 15 because of a weakened immune system. Ironically, it was Henry's paranoia of his only legitimate son dying from illness that caused him to die at a young age.
You can also boost your immune system through FMT which I recommend:
https://en.wikipedia.org/wiki/Fecal_microbiota_transplant
Most insurance companies aren't going to pay for elective ones though sadly.
lol, definitely always wash my hands. however, reading this thread.
it sounds like you literally get fecal matter ON your hands when you use the washroom. i mean, sometimes an accident happens, but this shouldn't be a common occurrence, lol. you arent wiping with you hand (are you?), you are wiping with a toilet paper, hopefully folded thick enough that you don't get anything on your hands.
urinals have splashback, but you shouldn't be wiping ur ass DURING #2, you should wait until things calm down so there's no splash back during wiping of a #2.
It is best to use plain water when cleaning yourself after defecation. 'Toilet paper' is treated with all sorts of non-organic solvents that do harm to the microbes in your GI and can cause an imbalance. Most of the world uses bidets and I feel this is the best way to remove excess organic matter after defecation. Just natural water. Unfortunately bidets are uncommon in the U.S. and are extremely rare in public waterclosets / commodes.