If we're just out on a lazy trail ride, I let my boy stop to poop. Usually during that time, I also have him on a loose rein and we're just moving along with no real 'work' going on. If we're working though, either on the trail or in the arena I expect him to continue on, pooping or not. Sometimes I have to give him a good squeeze to remind him, but nothing horrible.
My boy doesn't like to pee if someone is mounted, likely because he parks out so far I think he's going to fall over anyway, and he can't do that with a rider. He chooses to wait until I dismount if he can, but will go if we're stopped and he really needs to. Since we rarely work more than an hour or two without a good standing/stopping/rest break in there, I don't worry much about it. I know one gelding that does pee and walk at the same time though- he just sprays it everywhere, including his back legs.