One of my parents' cats does that, too. And get this--she's so considerate that she even provides gifts for visitors as well! My brother stopped by the house once and when he came back out to where his car was parked in the driveway, Chopper had thoughtfully left half a chipmunk by one of his front tires.
Try stepping on a catfish as you walk out the front door on the way to school.
My kitty loved to leave all sorts of creatures (some whole, some half-eaten) at our doorstep, but the catfish were the worst. The "wobbled" as you stepped on them. Lord bless her, she was a generous cat. 
I have been guilty of poop flinging, but only when I was 100% certain of the pooper. If I wanted animal poop in my yard, I'd run up to the mall and buy some at the Pet Poop Store. Oh wait.....There isn't one.....Because no one wants animal crap in their yard.
We ask nicely for the person to stop their animal from pooping in our yard and if they don't stop it, we kindly return the poop to their possession. Your neighbor (if indeed they left the poop on your doormat) could have avoided this mistake if they had just made certain it was/was not your animal doing the pooping. We've only had a few poop leavers in a few decades of marriage. Returning their "stray" poop always seems to stop the behavior. Then again, maybe they just think I'm a nut and want to avoid causing a meltdown.
As some have suggested, I'd just mention to the neighbors that poop was left on your doorstep and ask if they have been experiencing trouble with this sort of thing too. Follow up with, "I'd never let my pet do that to someone's doormat, and I can't believe anyone else allows their pet to do it." Then they'll realize the "pooped" the wrong person, feel like.....crap.... and that will likely be the end of it.
