Yes, there is often a sign on the door which says OPEN on one side and CLOSED on the other, and you can turn it around after opening and before closing the shop.
The point is, it says OPEN, not OPENED.
In a passive sentence, "The door was opened by Fred", this tells us who opened it, or that it has been opened, and that after this happened, the door was then open.
Here open is an adjective telling us the state of the door, but opened is a past participle, telling us what action took place.
When you are making a statement about the state of the door/room/shop, particularly over the course of a period of time, you have to use the adjective.
Oh, having just seen your later post, I see where your confusion lies. The problem is that the past participle of the verb "to close" is "closed", but the corresponding adjective of state is also "closed". That's just coincidence. Unfortunately when you see "closed" you don't know (except from context) whether it's an adjective or a participle. With "open" or "opened" you can tell the difference immediately even without context.