this is due to the MBTA (migratory bird treaty act). this is to protect native birds from being hunted for their feathers and other body parts. after all, it would be easy to kill a bird and say you ‘found’ the feathers. while it’s unlikely law enforcement will care about the cardinal feather you found in your backyard, it’s important to be aware of the law.
some birds that are not subject to this rule:
poultry
non-native pets – it’s okay to keep parrot feathers etc
invasive species – house sparrows, european starlings, etc