Goats can ram into armor stands moving them around the world.
Steps to Reproduce:
Disable mob griefing
/gamerule mobGriefing false
Place down an armor stand in an enclosed area
Summon one or more goats in that area
Wait for a goat to ram the armor stand, or increase tick rate
/tick sprint 1d
Reproduction Results:
The goat will ram the armor stand knocking it away from it's placed position, despite mobGriefing being disabled.
Screenshots:
[media][media]
Notes:
While armor stands are entities, they very often used for deccoration in building. Having goats be able to move armor stands can go against a players desire to not have mobs grief their builds.
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Comments

Goats can move almost every entity when ramming them such as zombies, creepers, cows, etc... I don't see the issue here as the goats are not "griefing" anything but I can confirm. As far as I am aware, the mobGriefing
gamerule is supposed to prevent non-player interaction with the world such as preventing endermen from picking up blocks and from creepers destroying the environment, etc...

My point is that armor stands are mostly used as a block to showcase armor. Just like the issue of creepers breaking them with mobGriefing turned off being valid, I would consider goats moving a block-like entity "griefing", like a goat entering your house and throwing your armor stand with fav armor off a cliff.

Can confirm in 1.17.1.

Are anyone aware of any other mobs that may have the ability to move armor stands?
Requesting ownership of thie issue to add future affected versions, and to update the description. (Original poster is inactive)