It is truly disgusting how some people choose to live, and we've all been there. Had it on my gloves, trousers, hose, boots.
Don't give up.
Where you know there's a dog, walk on the lawn in a straight line until you meet the first turd. STOP there and go back, that will give you the length of hose to work with and avoid the poo.
Watch out for cat excreta, as they do it in less obvious places, dogs just dump their guts where they fancy.