There is a lot of research on this. It's a deep, fascinating rabbit hole and I don't know its contours well enough to flag the entrances. But it touches subjects like mammalian postpartum depression, infanticide in great apes, why the characters :) make one go "aww," cute aggression and a host of other matters.
To address your point a bit more head on, I imagine public reactions to a publicly-defecating child would be very different from those to an adult.
Are you so out of touch with basic human desires that you don't see the difference between having _your biological baby with your genes_ and a random homeless person? That people love their baby _despite_ their poop, because of the joy they bring, and because it satisfies the most primary of biological drives (reproduction).
And you think it's weird that I'm okay with my baby's poop and not the poop of a random adult.