No, not a good idea- there are a lot of toxins (including carcinogens) in dryer sheets. They are, however, really good for dusting TV screens, and other surfaces. They actually help repel dust when used this way. Your best bet for the birds is lint, string, unraveled threads, etc.
I'm sure others know better than I but I'd not use them. The birds would carry them in their mouths and the baby birds would roll on them. Probably not a good idea.
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