Hi.
Can wild birds eat grass fed plain cheddar in small amounts.
I'm not quite sure what's prompted you to ask the question, however, nature generally will only eat what it's biologically designed to eat, unless there is a shortage of proper food that means to survive it has to diversify.
Mike
Flickr: Peak Rambler
I know people have included small amounts of cheese in home made pastry for birds, with no reported ill effects