I summon 4 NoAI foxes in Sitting, Sleeping, Crouching, and normal state.
When the fox with Crouching:1b NBT tag is in the scene or rendered, it will affect all the other foxes animation.
Although those foxes' NBT tags are Crouching:0b, they all sway their bodies, just like the one with Crouching:1b NBT tag.
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In the background, there're 4 NoAI foxes, and those 3 in foreground are alive. All of them will shake their body.
Please check if that's still an issue for you in the latest 1.15.2 stable release.