"The only droppings that can safely be used in the garden directly, without composting, is from rabbits."

I would add to that: goat, llama, and alpaca...pellet form manure tends to be more thoroughly digested which also means fewer weed seeds are likely to be present than in horse or cow manure.

In old time hot beds, fresh cow manure is dumped into a dug pit, covered with good soil and finished compost, and heat-loving plants are then planted. It's like an underground compost heap, and the underground heat generated can bring on crops in a greenhouse or in the garden without the dangers associated with fresh manure applied directly on and around plants.

Everything depends on where the manure came from, what those animals are fed and how they are cared for, and how it's handled in your garden.