Sure in Western myth and religions the god have afinities with animals, and often turn into animals. That is not what is being discussed. What we are talking about is very specifically the portrayal of gods as "humans with animal heads". I'm having trouble finding any examples of this in western culture.Most Greek/Roman gods turn into animals at some point or another or at least have "favored" animals (peacocks and cows for Hera, bulls and eagles for Zeus, owls for Athena, horses for Poseidon, leopards for Dionysus, etc). It's not the same as being drawn with animal heads, but it's pretty close.
Then there's also The Morrigan with ravens, Loki with snakes, and lots of other examples of gods/spirits from European mythologies transforming into or having strong connections with animals.