I asked myself the same question when I started riding through suburbs and public walking trails. I was quite paranoid about getting yelled at by some upset jogger, and had also thought about the possibility of "horse diapers." I talked to my BO a bit about it, since she has been riding horses in this area for 30+ years, and said she has never had anyone get upset so long as she kicks it off the trail. And so far, that's the same experience for me.
I have been blessed with a horse who thinks it's funny to poop on the narrow walking bridge. So then I need to dismount, walk back, and kick it off the edge of the bridge while my horse patiently stands with me. Sometimes a few people accumulate on either end to wait for the crazy girl to finish kicking poop off the bridge. No matter how hard I try, there will always be some remnants left in the cracks of the wood. So far, no one has complained - they probably think it's a comedy act.
One time, she pooped right in someone's driveway right in the middle of the development we walk through to get to the trails. A middle-aged man walked onto the front lawn and, seeing me, said "Don't. Move." And ran inside. I thought "uh oh, this is the grand moment of shame I've been expecting." Turns out his wife just loves horses and he wanted to prove to her that he wasn't crazy when he said "Honey, there's a horse walking down the road!!" the week before
turns out she has her own horse and was more than willing to shovel the poop for me, even though I offered to do it myself.