"It's" in many cases is an impersonal expression, like in French "c'est".
Impersonal expressions are those which do not have a specific subject. In grammatical terms, "impersonal" does not mean cold, but rather invariable by grammatical person.
It's hard to speak. (Speaking is hard)
It's good to drink a lot of water
It's probable that David is doing it.
It / That is good to know.
It / That is impossible to find.
It's to be hoped
and so on.
"It's" might be followed by a noun in the plural, informally. In your example, "It's not anemones, it's animals", there's a strong possibility that the sentence has a subject. Hence, the correct way to say is:
"They are not anemones, they are animals.".
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