As I know, animals can be called "he" or "she" (not only "it").
Also, if a person's gender is unknown, we may use "they" instead of "he" or "she".
Is it possible to use "they" when we talk about a specific animal and in what context?
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I don't see why you couldn't use "they" for an animal of unknown gender. However, it's less necessary than when referring to humans, because there's not as much compunction against using "it".
Some people like to consider pets to have almost the same status as family members, so they may prefer not to use "it" for these animals.