Why are canines not nauseated by similar foodstuffs/state of decay as human beings?
Your dog finds these things palatable, I assure you, and no gag-reflex suppression is needed.

I had a dog that would steal duck eggs from my flock, bury them all over the place, and dig them up when properly rotted to enjoy as a treat, and no, I'm not making this up. I saw her do it, ran across many buried duck eggs while gardening, and could immediately smell when she was enjoying one.

All that to say what smells good to a dog has nothing to do with what is acceptable to you. Many of your "dislikes" are conditioned: living in a society where cleanliness is valued and clean water is available, humans in such societies can afford to snub their noses at less sanitized things.

Manure may well elicit a completely different reaction to a farmer, who saves it carefully before spreading it on his fields to enrich the soil. To him, it might be the smell of a good crop next summer.

Many species exhibit corprophagia. It's not known why dogs (some, far from all) do this. Rabbits, for instance, eat their own feces after their first movement of the day. This is normal and nutritional for them.

Eating the feces of other species, particularly herbivores, is common among dogs and isn’t considered abnormal, just undesirable. My (same) dog followed my goats around like they were Pez dispensers. Since dogs can't digest cellulose, they get some of the advantage of eating plants this way.

Capybara, rabbits, hamsters and other related species do not have a complex ruminant digestive system. Instead they extract more nutrition from grass by giving their food a second pass through the gut. Soft fecal pellets of partially digested food are excreted and generally consumed immediately. Consuming these cecotropes is important for adequate nutritional intake of Vitamin B12. They also produce normal droppings, which are not eaten.

Young elephants, pandas, koalas, and hippos eat the feces of their mother to obtain the bacteria required to properly digest vegetation found on the savanna and in the jungle. When they are born, their intestines do not contain these bacteria (they are completely sterile). Without them, they would be unable to obtain any nutritional value from plants.

Eating garbage and human feces is thought to be one function of dogs during their early domestication, some 12,000 to 15,000 years ago. They served as our first waste management workers, helping to keep the areas around human settlements clean. A study of village dogs in Zimbabwe revealed that feces made up about 25% of the dogs’ overall diet, with human feces making up a large part of that percentage. 

Coprophagia
Daily rhythms of food intake and feces reingestion in the degu, an herbivorous Chilean rodent: optimizing digestion through coprophagy
Coprophagia as seen in Thoroughbred Foals