Thanks for providing a photo of the button after some cleaning to reveal more details of the emblem. Sorry, but those details confirm it is indeed a civilian-usage imitation of an actual US Navy button.. as Creskol suggested. (The imitations are used on civilian copies of Navy PEA coats and other "nautical-themed" clothing, including yachting-jackets.) Note that your button's "rope border" does not pass through the loop on the anchor's top, as it does on actual US Navy buttons ever since the present-day emblem was adopted in 1852. See the photos below, showing a gold-gilted civil war era US Navy button.
I should mention, on US Navy buttons, the eagle's head was turned from facing the eagle's left to it's right in 1941.