After every reset, the door to the Pool Shrine, now named Shrine of Bane's Grasp, is always unlocked, when I would think it should start off locked.
I think the shrine is supposed to be 'open for all' to go in and pray. Only the door for the small chamber with the chest is supposed to be locked all the time.
This is the same for the Crystal Shrine and may not be a bug.
I believe there is reason behind it though, since after setting your spawn point you will spawn inside the temple doors. So if for some reason the tenancy is lost and the key is made defunct, you will at least be able to exit.