Hinduism have various Gods who they worship and have divergent personalities and appearances depending upon the visualization and the ways they are illustrated in the legends.
Let us take the example of Lord Ganesha who has the head of an elephant. Lord Ganesha was perceived in that way by all his devotees and sadhus so nobody has felt the need to mistrust or drill into details. Without questioning the facts, we worship him as it a set pattern and we are following it. This query has got different answers
First section believe that Lord Ganesha is a living being with the countenance of an elephant.
Others believe that the elephant head is symbolic to represent him as the God of Obstacles, though he is the most popular deity loved by a wide section of the society ranging from kids to old people.
There are different stories which tell us how he got this appearance. The Puranas ( ancient Hindu texts) describes how Lord Ganesha got the elephant tusk and story is related to his birth which explains that Lord Shiva and Parvati created him. Ganesha is considered as the remover of obstacles who provides success, prosperity and fortune.
Various other Hindu deities have animal features like Lord Hanuman, Varuna, Kamadhenu, the Nagas, the Vahanas (animal mounts of the Gods) and four of Vishnu’s ten incarnations (fish, turtle, boar and half-man-half-lion).
Explanation: After studying and investigating these facts further, it has come to notice that Hinduism alone do not have deities with animal features whereas the ancient Greek gods including God Pan, who has the hindquarters, legs and horns of a goat, and the Sea Gods Ichthyocentaurs, with human heads and torsos, the serpentine tails of fish and the front legs of a horse. Further it can be seen from Egypt’s pantheon that Anubis (God of the Underworld) is a falcon-headed man, as is Ra (the Sun God). Thoth (Lord of Wisdom and of the Moon) has the head of an ibis or a baboon, and His consort, Bastet, has the form of a cat or a lioness. Quetzalcoatl, a feathered serpent was worshipped by the Mesoamerican people.
Even in Buddhism and Shintoism – Kitsune the fox and Tengu the bird man are considered as the powerful beings who can shift shapes and can easily transform into animate or inanimate shapes to befool humans. In Japan, many shrines are guarded by Komainu or Shishi (pair of magical lion-dogs)
In Christianity, the angels which are depicted in the stories are half-human and half-bird. In early Christianity the four-headed beings called Cherubims were significant part of the religion. And it is mentioned in the Bible’s Book of Revelation where John writes, “I saw a throne standing in heaven; and the One who was sitting on the throne… In the center, grouped around the throne itself, were four animals with many eyes, in front and behind. The first animal was like a lion, the second like a bull, the third animal had a human face, and the fourth animal was like a flying eagle. Each of the four animals had six wings…” (4:1-8). All these are considered powerful in the pantheon and pretty close to the maker.
The fact is that in most of the religions, the practice of worshipping the gods with animal features is not followed as of now. But in Hinduism , Deities with animal features are worshipped with zeal and zest.