Disease risk? For some reason people seem to think that if it's poop, then it must be disease ridden. My own husband treats any kind of poop as though it is toxic waste to be avoided at all cost. Good thing we never had a baby!
I worked in veterinary medicine my entire working life. I advised pet owners to avoid feeding their dogs raw foods if they wanted to use the poop as a fertilizer. Salmonella wasn't much of a problem 30-40 years ago, but meats and eggs of today have a far greater percentage of contamination problems. Commercial meats also are contaminated with other disease agents including antibiotic resistant bacteria. It makes no sense to me to
feed raw commercial foods to my pet, thus introducing those problems to my own farm. Keep the pet's diet clean and they won't be welcoming those disease issues to your pasture.
Intestinal parasites are also a concern. As a caution I deworm every dog that is added to my own farm, cleaning up the poop immediately for several days so that any eggs being passed do not contaminate my land. New dogs get dewormed multiple times to completely eliminate worms. They are then routinely dewormed as the situation mandates. For example, I dewormed my dogs when they first arrived. I test for worms off and on but have never found a positive dog (except for one that once picked up strongyles from the horse) since the initial deworming. But then again, I don't allow other people's dogs on my farm since they very well could poop worm eggs.
With my own dogs, as long as I keep them clean I have no fear using the poop in my compost.