This makes no sense as you should not be taking fall damage from the stalagmites, but rather the stalagmites hurting the player because of their sharpness
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The damage from stalagmites seems to be fall damage technically, which is probably why it is affected by the gamerule. This also causes MC-206555 to be a thing.
I have done some research and I can say that stalagmites work exactly like hay (well, or bed / honey) They just change the fall damage in%. Falling on hay takes 20% of normal fall damage. Falling on the bed 50%. Falling on the stalagmite ~ 500%. This means that the iron golem, cats, chickens, a player with a feather falling will not take damage from stalagmites AT ALL
I can confirm.