The direct answer for a green-cheeked conure
It is not safe for a green-cheeked conure to eat food made for other kinds of pets as part of its routine. A green-cheeked conure is a small, energetic parrot that eats seeds, pellets, fruit and vegetables in modest amounts, and its nutritional balance is easily tipped by rich extras. Dog and cat foods concentrate fat, salt and animal protein for carnivores, rabbit and guinea pig foods are fortified for grazing mammals, and none of those recipes was built around a conure's liver, kidneys or gut. An accidental taste is one thing; a standing invitation at another pet's bowl is another.
Why conures find other bowls so easily
A green-cheeked conure is famously hands-on: it explores with beak and feet, squeezes into gaps, and investigates anything the household treats as interesting. During out-of-cage time it will shoulder in beside a cat at its dish or carry a piece of kibble off to a curtain rail to work on at leisure. Conures also bathe and dunk, so a water or wet-food bowl belonging to another pet is doubly attractive and doubly contaminated. Because the bird is small and quick, raids often go unnoticed until they are a habit, which is why the feeding layout of the whole home, not the bird's obedience, is the thing to fix.
The specific risks for a small parrot
Richness is the slow risk for a green-cheeked conure: regular kibble snacks add fat and salt that push weight on and load organs sized for a leaner diet, while mammal vitamin premixes eaten alongside the bird's own food can overshoot fat-soluble vitamins. Bacteria are the fast risk. Wet pet food standing in a bowl, raw diets especially, can carry organisms that cause serious gut infections in birds, and a conure feeding there also contacts the other animal's saliva. Even dry food stored badly is a hazard, since a conure chewing into a bag shared with pest activity or moisture can reach mouldy pieces at the bottom that nobody would have served it directly.
After a conure has eaten another pet's food
Retrieve the green-cheeked conure, refresh its own food and water, and think back over what it actually took: a crumb of dry kibble calls only for watching, while a session at a cat's wet food deserves closer attention. Over the next day, healthy signs are normal droppings, bright behaviour and a good appetite at its own servings. Contact an avian veterinarian if droppings change and stay changed, if the conure regurgitates, goes quiet and fluffed, or loses interest in food, and do so sooner if the food eaten was raw, spoiled or had stood for hours. In a bird of this size, a day of not eating is significant in itself.
One feeding plan for the whole household
Give every animal a defined place and time: the conure fed in or on its cage, dogs and cats fed with bowls lifted afterwards, and no all-day grazing dishes left where a flying bird can reach them. Store each pet's food in its own sealed, hard container, since a green-cheeked conure can chew through a bag left on a counter and spoil the contents for everyone. Keep the conure's own menu varied and its foraging toys stocked, and a bird busy with its own food works less hard at stealing. KinsLe Care Teams can hold the whole household's feeding plan in one place, each pet's meal assigned and timestamped, so the conure's separate routine survives schedule changes and stand-in feeders.