I am sorry but that doesn't mean anything to me. To me, a bird is a bird, just like cats are the same as well as dogs. What is there physically which will prevent it? As I said genetics I did not understand.I'll do my best @Gypsy
In one of your examples, you used a hyacinth x blue and gold macaw. Taxonomically, a hyacinth is:
Order: Psittaciformes
Superfamily: Psittacoidea
Family: Psittacidae
Subfamily: Arinae
Tribe: Arini
Genus: Anodorhynchus
Species: A. hyacinthinus
Binomial name: Anodorhynchus hyacinthinus
A blue and gold is:
Order: Psittaciformes
Superfamily: Psittacoidea
Family: Psittacidae
Subfamily: Arinae
Tribe: Arini
Genus: Ara
Species: A. ararauna
Binomial name: Ara ararauna
Now, they are both still MACAWS, even though their genus is separated. The Subfamily Arinae refers to Neotropical parrots from South America. Within this Subfamily is also the conures. A sun conure is, for example:
Order: Psittaciformes
Superfamily: Psittacoidea
Family: Psittacidae
Subfamily: Arinae
Tribe: Arini
Genus: Aratinga
Species: A. solstitialis
Binomial name: Aratinga solstitialis
So see how a hyacinth and a sun conure are both only one small step away from each other (separated by genus). Let's now look at an Indian Ringneck:
Order: Psittaciformes
Superfamily: Psittacoidea
Family: Psittaculidae
Subfamily: Psittaculinae
Tribe: Psittaculini
Genus: Psittacula
Species: P. krameri
Binomial name: Psittacula krameri
The Ringnecks split off on the parrot family tree starting at Family. That is 4 steps removed from the sun conure, where the hyacinth and blue and gold are just one step removed.
This is true of other animals if you look, with some even closer related. Tigers x Lion are only separated at the species level (they are both from the Genus Panthera; Lion is Panthera leo, a tiger is Panthera tigris.) A zebra is Equus zebra while a Horse is Equus ferus. A dog is Canis lupus familiaris while a wolf is Canis lupus.
So, a sun conure and indian ringneck are simply not related close enough to be able to hybridize. A conure and a ringnneck are as closely related as you are to these gibbons: