Can an interrupting settlement allow opponents to move previously unmovable ships?
No, you may not move it, your ship is not open. From the official site.


  A ship is “open” when it is located at the end of a ship route. As soon as a ship route connects two settlements, the ship route is considered as closed. A ship in a closed ship route can not be moved. This rule also applies if another player builds a settlement on the intersection of your closed ship route. In this case, the continuous road is considered as interrupted in terms of being counted towards the Longest Road; however, the two settlements of the ship route are still connected, meaning that the ship route remains closed.