Running offroad: if my dogs crap on a well worn path I'll remove it. If they crap a reasonable distance off the path I leave it there. The places we run, there is a fair chance of stepping in cow shit, horse shit, cat shit, sheep shit, chicken shit and (worst of all by a million miles!) the ultimate stink of fox shit. With all the other shit already there to contend with, I can't see the odd dog shit as a huge problem...
My own bugbear is horse shit left on my local bike path. Some piles are over a foot high and can cause crashes for winter cycle commuters as its hard to spot in the dark. I don't think anyone ever got a head injury from crashing on dog shit.
I dislike seeing big piles of dog crap but at least it breaks down eventually. Litter such as discarded gel wrappers and energy drinks bottles piss me off much more.
Here's a question though: With the new biodegradable poo bags which do actually break down in an eco friendly manner, when running or walking on hills and mountains all day (i.e. not wanting to lug a bag of poo about with you for 8+ hours) is it acceptable to bag it up then lob it a good distance away from the path?