My dad is a pensioner now, and got put in a lovely bungalow by local housing association. It came with with a lovely garden, and he was really excited by the prospect of a cherry tree.
Well, the cherries are ready, and the birds ate the lot!
I used to have a cherry tree in my garden. I was sitting in the branches picking cherries, when I saw a blackbird (not an SR-71) sitting on the outer twigs eating cherries I couldn’t reach. He had a look in his eye that said “these are my cherries and there’s nothing you can do about it!”
Then a sparrowhawk took him out in front of me and ate him. That’ll teach him.
What makes you think birds wouldn't still recognize moving zombies as a potential threat just like living humans or any other larger animal and just stay clear of them? Also, the possibility of zoonosis isn't all that far fetched either, resulting in zombie birds also spreading the plague