Yeah I'm a mod and I'm a fucked up degenerate wanker. Sue me? To answer your hypothetical question, no I wouldn't perform a surgery without first scrubbing and having gloves on. Who the fuck would? That's so off-league it's ridiculous. Taking a shit, having all this particulate matter on your hands full of pathogens, and then going in touching the internal organs of somebody means for the most part avoiding their primary mechanism of protection from bacteria and other pathogens - the stomach. Since when I shit and eat I don't avoid it, and given my pretty good immunity given years of this practice, I dare say it's pretty a-ok.
I guess it will come as a sort of a surprise to you that I used to work (resuming soon) in organic synthesis in chemistry where cleanliness is very important, and I always work with clean hands and with gloves.
The OP question was "is washing your hands really necessary after taking a dump?". The answer is no. Me and many more in this thread, including the OP, don't, and we're bloody fine. And that answers the "really necessary" part.
Wipe it on your pants. That's what I do. Yeah I'm a fucking animal.