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What is this and why does it have a door?
Answer:
This is by the entrance to the queue for the Alice in Wonderland ride. This mushroom is one of a few old ticket booths still remaining in Disneyland, from the days when you needed a separate ticket for each ride.
The responses I received were:
Tim & Malinda
It's the control for the Alice in Wonderland ride.
-- That's the correct ride, but the controls aren't in the mushroom.