Yes. The law, and the desire to protect birds and to protect the ecology we humans need to survive and thrive, says to keep feathers in the environment.
By the Migratory Bird Treaty Act of 1918, there was an “establishment of a Federal prohibition, unless permitted by regulations, to ‘pursue, hunt, take, capture, kill, attempt to take, capture or kill, possess, offer for sale, sell, offer to purchase, purchase, deliver for shipment, ship, cause to be shipped, deliver for transportation, transport, cause to be transported, carry, or cause to be carried by any means whatever, receive for shipment, transportation or carriage, or export, at any time, or in any manner, any migratory bird, included in the terms of this Convention . . . for the protection of migratory birds . . . or any part, nest, or egg of any such bird.’ “
And, as the US Fish and Wildlife Service says on the page Migratory Bird Treaty Act: “The Migratory Bird Treaty Act prohibits the take (including killing, capturing, selling, trading, and transport) of protected migratory bird species without prior authorization by the Department of Interior U.S. Fish and Wildlife Service.”
Some people may keep feathers and nests and such, if they are granted a license to do so by the US Fish and Wildlife Service.
Some birds — invasive species or game birds (you can, of course, keep what you had a license to hunt!) — you can keep feathers of. A list of protected birds is here: