If the dog poop is on the bottom of the shoe you can use a stick to scrape it out of the treads. If treads are too small try a tooth pick. also waiting till the poop dries then banging the shoes on a hard surface such as the sidewalk.
You need to get as much poop off the shoe as possible. You can use a hose or find a puddle. Then place your shoes in the dishwasher on the pots and pans cycle. If you don't have a dishwasher, use hot soapy water with a scrub brush.
Hose them off outside and use a paper towel to scrub if needed. If that doesn't work, you can put some types of shoes (not sued or leather) in your washing machine in a garment bag.