The Orthodox Catholics won't use statues in their churches because of this. They use paintings instead.
I think it's kind of a stretch to think that this might apply to stuffed animals myself, but some might differ.
One tactic you could use, which has been adopted by some of the members on this forum goes like this. You read carefully through the entire New Testament and if you find no mention of stuffed animals, you know they're not allowed.

May The Sheep Be With You
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Proud parents of our own "Daddy's Little Girls"
I heard Jesus He drank wine and I bet we'd get along just fine.
He could calm a storm and heal the blind and
I bet He'd understand a heart like mine.
Miranda Lambert