This door in Ardougne becomes a gate when opened, not only that but the "pick lock" option functions as the "open door/close door" option regardless of whether you have a lockpick. When closed, it appears as a normal door.
(https://i.imgur.com/nPPapxB.png)
(https://i.imgur.com/J3eA1gJ.png)
EDIT: and although the door appears as a gate, it still knows its a door. It has no "close door" option however
(https://i.imgur.com/iGtG1Nk.png)
There seem to be quite a few doors/gates like this, sadly. I'm sure if other gates actually opened they would also have similar problems.
Should be fixed next update