There are layers of truth here. There's a term called hybrid vigor, which refers to the increased capacities of some mixes. A mixed breed dog, for example, probably has a better set of genes than a purebred in many cases. Purebred dogs, cats, etc are selected to conform to the appearance of the breed standard, but mixes will have better resistance to genetic disorders and are sometimes stronger and healthier. But dogs are all the same species, as are humans. Mules are examples of true cross-species hybrids that combine the size and strength of a horse with the intelligence, hardiness, and temperament of a donkey. But they are sterile. Parrots are actually different species, so hybrids could be infertile. The main problem is what Sailboat said - many parrots are going extinct in their home ranges, and may depend on the offspring of captive bred birds to restore the wild population. If the captive birds are allowed to hybridize, there won't be genetically pure individuals to release. Also, since different parrot species evolved to survive under specific environmental circumstances, a hybrid individual might not be able to survive if reintroduced into the wild.
Cross breeding is a luxury humans exercise to create animals for our amusement and needs, such as sheep herding dogs or rat catching cats, and not something we can afford for a diminishing population of a species. So I wouldn't hesitate to adopt a hybrid bird, and the bird bears no blame obviously, but I don't condone the breeding of such birds. It's vanity and selfishness.
