Benjamin is a cynic who doesn’t adhere to any “ism.” He doesn’t believe any change in power will lead to significant change in the conditions of life.
Since Napoleon, via Squealer, frequently changed the tenets of Animalism to suit his personal and political needs, it is tough to say who lived by the philosophy of Animalism. But, as far as the original idea of Animalism, which was to give power to the animals, I would argue that Old Major, Snowball and Clover lived most faithfully to the original idea.
As Napoleon changed the commandments of Animalism, the one who stayed completely loyal was Boxer. He did not have any philosophical interest in the ruling ideology. His heart was in the right place and he wanted conditions to improve, but I think his loyalty was to the other animals: not Animalism in its beginning or eventual corruption. He remained loyal to the initial idea of Animalism but his strong loyalty prevented him from seeing Napoleon’s increasing corruption of Animalism.
If you mean the original idea of Animalism, analogous to Marxism, then I would say Old Major, Snowball and maybe even Clover lived closest to that philosophy. The original idea of Animalism was to clearly separate Animals (Marxists) from humans (Capitalists), primarily to give power to the animals (workers). Napoleon, Squealer and their entourage eventually became more "human" by taking all the power for themselves.
Old Major provided the initial philosophy and motivation. Snowball put it into action. Clover questioned things when Napoleon began to change the commandments. To me, these three characters did the most to start and sustain that original idea of Animalism.
In the end, Napoleon essentially changed Animalism into its opposite. By the end, he physically and politically resembled humans. Napoleon was the least faithful to that original philosophy of Animalism.