Parrots don't have morals. They don't care if they breed with their siblings, their parents or anyone else they may be related to. In captivity or in the wild.
You can have two of the same species of birds together and they may never mate. Even if they do mate, they may never lay eggs. (I know of a cockatiel pair who have been mating for over a year, and no eggs!) Even if they do lay eggs, the eggs might not hatch.
Usually, as long as you don't encourage them to reproduce, they wont. If they are really interested in reproducing, you can take measures to try and discourage them from reproducing.
Currently, I have a lone mitred conure (caged alone). I wish I could have gotten him and my cherry head, prior to his passing, to get along! But alas, opposites did not attract in this case. In another cage, I have 4 cockatiels and a bourke parakeet. Out of all the birds in there, only one is a male, and that's one of the tiels. Unfortunately, he lost his long time mate last year, and although he's paired up with another hen, there's been no interest in reproducing between the two of them. I'd rather keep it that way anyway, since I'm not interested in breeding.