I think if a bird effectively had a human mind, it absolutely could be a fascist. I don't really think morphology or genetics are meaningful indicators here.

The reason fascism is only a human concept in our world is that, as far as we have any evidence to believe, it (as well as any other "grand" political ideology) is something only human consciousness is capable of among surviving species. The fundamental political dynamic is not necessarily tied to species, we just see that in our present world only humans are capable of ascribing to it.