There are five distinctive ID-clues for your unknown button showing an anchor and having a "rope border."
The first is for time-dating.
1- it is a 2-piece button with an emlem impressed into its thin sheetbrass front. That dates it to no earlier than about 1830. I mention that because its construction excludes it from being a pre-1830 British Navy button, which it closely resembles.
2- The "rope border" is
extremely large -- let's call it way oversized.
3- The anchor is shown inside a Roman block-letter "O" -- which is not merely a circle. Note that its sides are fatter than its top and bottom.
4- The anchor is shown on a horizontal-lined background.
5- The anchor-rope's position (it loops to the viewer's left below the ring at the anchor's top) and the rope's length (it does not extend below the anchor).
I mention all those characteristics so you will keep each of them in mind as you search through allthe photos of "Navy" buttons on the following (single) webpage:
Navy buttons
I found several very-close matches there... but no
100%-exact match. In my opinion, the closest match is a 20th-Century British "Merchant Navy" -- equivalent to America's "Merchant Marine" service. Merchant Navy buttons are considered "nautical" buttons but not Military ones.
The "very-close" matches on the linked webpage are:
Austria Merchant Navy
British Merchant navy
German Kriegsmarine World War 2 (Military Navy)
But... some of those lack your button's lined background, some show the anchor inside an ordinary circle, or the rope-border isn't nearly as large, or the anchor-rope doesn't match.
Lastly, your button appears to have an iron/steel sheetmetal back (with a cheaply-made non-soldered iron wire loop). That construction, in combination with the apparent inability to find an exact match among actual Military Navy or Merchant Navy buttons, suggest it is what you suspected... a 20th-Century civilian-clothing "Fashion" button.
