It can be observed that many Hindu Gods and saints are shown sitting on animal (tiger) skins. What could be the reason behind this?
Lord Shiva is shown sitting on or wearing a tiger skin. The tiger is the vehicle of Shakti, the Goddess of power and force. Shiva is beyond and above any kind of force. He is the master of Shakti. The tiger skin that he wears symbolizes victory over every force. Tiger also represent lust. Thus sitting on Tiger skin, Shiva indicates that he has conquered lust.
It also signifies non-lavished life style of Lord Shiva.
For the Yogi's, Most of the yogi's origin is said from Shiva, That's why they have similarities in style to Shiva.
It's prescribed in Ayurveda not to sit on bare floors because of the risk of Vata. Hence, the reason for Yogis to use some kind of separation between themselves and the floor/rock etc.
Moreover, since Yogis and Sanyasis are generally away from civilization and man made fabric, it could also lead to the use of more natural and available 'fabric' of animal skin.
I found this from a yogic site,
It is traditional for many Kundalini Yoga practitioners to use sheepskins on which to do their yoga. This is personal preference. Yogi Bhajan recommended the sheepskin for meditation, as it created an insulation between the yogi and the magnetic pull of the Earth. Indeed, many people experience deeper states of connection to their Self and the Universe when using a sheepskin as compared to a sticky mat or cushion (synthetic yoga mats are taking up to 1/3 of the aura away from a person).
“Only yogis who lead a strictly celibate life use tiger skin. The others use antelope skin. The reason for this is the difference in the power of the respective skins to isolate earth magnetism”. - HathaYoga Pradipika commentary.
And another widely believed opinion is it is symbolic for as the yogi has shed all the Rajo gunas and conquered the animalistic instincts of a wild beast.
Not all Gods are shown sitting in tiger skin. Usually Shiva is shown, since Shiva is a metaphor for "Destruction & recreation".
Again, I repeat that the Western religions have this digital view of wrong and right.. I know where the question is going , but let me put it in perspective..
"Animal rights", "Vegetarianism", are all concepts which evolved along the way. 4000 years back, we can only speculate how these value systems evolved. There were societies which had a iron grip on what constituted wrong and right, and Hindu society was basically, a non-prescriptive, debate and conflict based society. So, there would have been a time, when kings wore animal skins, and therefore when artists painted God, they would have painted God as sitting on animal skins.
Now, we have 1000 tigers in the whole planet. So, we don't even want to see a God sitting on an animal skin.
Today, I can guarantee that very very few Hindus would purchase animal skins in their homes. Now, that's an evolution of opinion due to the current world context. But that does not mean, a Hindu would repaint the Shiva pictures and remove the animal skins and replace them with vinyl carpets.. That's a religious symbol..