When a man and an animal become one there is a blending of instincts and abilities, but underneath remains our core primal needs.
The short answer is yes, but it would be a highly debated process and would evolve throughout the years.
A horse pooping in a toilet is an hilarious image, and a man pooping in the middle of the street makes you question his sanity, but alas, a centaur could get away with both. As centaurs fist started assimilating with our society people would understand and tolerate encountering their poop, much like we tolerated horse poop in the street back in the wild west. However, throughout the years people would get tired of the smell and stepping it and cleaning their shoes. “I just bought these shoes!” – someone would probably yell post poop stomp.
We eventually would setup designated pooping areas outside for centaurs. These would work well for a while until the poop started to build up. Let’s be honest, no one is picking up after a centaur because a centaur is owned by no man. Eventually we would need more sophisticated outdoor stall for centaurs that included their own sanitary sewage filtration system. We would agree to do it until we realized that it is a tax coming out of our pay checks. “I’m not paying for their poop!” – someone would probably yell as they were filling their taxes.
However, would this be enough? Could a centaur control his poop like a man, or would their primal urges overcome intellect causing them to poop when they needed to, without hesitation. Have you ever tried telling a horse not to poop? “Hey you’re not supposed to poop there!” – someone would probably yell.
If they could control their urges as centaurs started coming more integrated with our society, and heading indoors we would have to add another stall that would be large enough for a centaurs to poop in. This would be a magnificent stall, bigger than all the others in the bathroom. When it was free of a centaur humans would try to poop in it because of its magnificence, and would feel guilty and ashamed when the left the bathroom if a centaur was outside waiting to poop. “Oh, I’m so sorry, I didn’t know anyone was waiting” – someone would probably say.
You are probably asking yourself a few questions, like, what is a centaur doing inside a building with a toilet? Do they have toilet paper or are they using a bidet? And about a million other questions that all of you too clever for your own good individuals will come up with.
If centaurs did exists one would have clearly sold out to some major corporation by now. Endorsing Nike horseshoes and Oat Bran, featured in movies, rolling through town with a posse in a carriage he was pulling. All of the meetings would be inside, movie shoots as well. When the centaur who sold out would go back to the forest on holidays to visit his parents he would tell them all about the glorious stalls and how he has the right to poop both inside and outside. All of the younger centaurs would find this cool and follow suit. “I am the poop king of the world” – a young centaur would probably say.