I don't get the false equivalency between your arm and your anus. The anus is neatly tucked away, and is supposed to handle fecal matter. You're not going to accidentally rub your unclean anus on some food or in your face, unless you cook differently than most people and is more flexible.

Would you put your face in your shoes for hours at a time, or rub it on the ground when you walked? Probably not, but thats no problem for the feet, because they're a different body part with different strengths and requirements.

That's a common argument, and a flawed one at that IMHO. If a bird pooped on a table, would you rub it off with your bare finger with some soap water, or would you use paper? (Granted, even this might give you the hint that dry paper isn't always the best idea.)

Well no, the whole point is that there's shit on you in the first place already, not touching it is not an option.

You clean your arse with water so that it's clean and not just wiped with paper, just as you afterwards will wash your hands instead of just wiping them on a paper towel.

Well, that comes down to cultural or personal preference. Some cultures consider feet unclean. Some people consider the anus unclean. How clean you try to make a body part depends on how clean you consider or expect it to be.

Soap and water. Never just water alone.

If a bird pooped the human way (same diet and result) the solution would be a piece of dry paper or leaf