You could be right about it being a Comtinental Navy button, but those are usually one piece. Mine is a two piece. I've looked everywhere on the Internet to find anything that looks similar to mine and I've found nothing
I think your button is a civilian fashion one. A few things point me in that direction. One is the basket weave background. Another is the lack of detail and the overall quality of the button and finally the lack of a backmark all lead me to believe it is not military.