Finches are often breed in large group aviary. They are less likely to have vet health screening. They can have air sac mites, like I think it's endemic in their population, but only causes the finch ( except some species of finches are more susceptible) issues if they are compromise, by nutrition, over breeding, other stressors. While most parrots haven't been exposed to them before, and more likely to cause health issues in otherwise healthy parrots.
They are more likely to have coccidia or carry other parasite. As well as different bacterial diseases , viral diseases. Often as carriers . That can sicken/ and or kill parrots .
It's generally not a good idea to mix different classes of birds like this for health reasons. Beyond the mentioned physical threat .
