Lilac Crowned Amazon (Bacci- Forever on my shoulder, forever in my heart.)
Yellow Collared Macaw (Loki the Monkey Bird)
Military Macaw (Wingnut)
Citron Crested Cockatoo
(Knuckles)
Usually missing toes that you see are caused by accidents or the parents bit them off while young. Some occasions are due to their genetics, IF caused by genetics, they shouldn't be bred anyways.
I think in nature toes that are missing due to an accident or injury could affect the ability of a bird to find a mate because there are plenty of other potential mates with all their toes. Kind of "survival of the fittest" type thing. In captivity, since there is usually not a large pool of potential mates to pair up with, it probably doesn't make as big of a difference.
Congenital defects probably can affect fertility, as the missing toes are likely just an outward sign of a bigger genetic issue. I don't think genetic diseases are studied much, if at all in parrots, so I doubt anyone knows what 57 disorders missing toes could be linked to and how to test for those disorders and figure out which ones affect fertility. Heck, they barely understand genetic diseases in humans...
Presently have six Greenwing Macaw (17 yo), Red Fronted Macaw (12 yo), Red Lored Amazon (17 y.o.), Lilac Crowned Amazon (about 43 y.o.) and a Congo African Grey (11 y.o.)
Panama Amazon (1 Y.O.)
Well in the case of the Male Hyacinth I used to play with, he was rather insistent on mating, when she was not in the mood, which is how he came to lose the toe in the first place... SHE SAID NO, AND NO MEANS NO!
So, at least on that occasion it prevented him from mating, but they have since had several clutches, so I'd say this one is probably a myth. But it would depend on the extent of the handicap, I guess.