I believe that Hinduism could be regarded as both Atheistic and Animistic / Pantheistic, depending on how one defines the word "God". From my article The Atheistic approach to God… or how to bridge the gap between Atheists and Theists :
An Atheistic perspective on Consciousness
We know from evolutionary biology that multi-celled organisms evolved from single-celled organisms. It is unclear to what degree single-celled organisms gave up their autonomy to be able to act as a single organism and it is reasonable to suggest that our individual cells have maintained some degree of autonomy (consciousness) that we are totally unaware of. A lot of human behavior is associated with subconscious processes in the prefrontal cortex that psycho-analysts refer to as the super-ego. This super-ego reflects the internalization of cultural rules in the form of memes. Such memes often influence human behavior in ways individuals barely realize and can be considered a form of collective consciousness. A group of humans that is connected by means of memes can act as a single conscious organism, much like a cell of our body can act as a single conscious organism. This and many other factoids directly imply that consciousness is not so much a product of our brains but rather a product of complexity and connectivity. From that perspective, the concept of consciousness can both be reduced to the molecular level and expanded to the universe as a whole, with the universe as a very complex holographic quantum computer
The relationship with Hinduism and Animism
In Hinduism, death is understood as the collapse of the Ātman (individual consciousness) and its dissolution into many different other components that make up the Brahman (universal consciousness). If you look consider the Trimurti (the Hindu triniti), one can clearly see them as anthropomorphic representations of nature (Vishnu) and its two fundamental opposite forces: emergence (Brahma) and entropy (Vishnu). Similarly, many other Devas (Gods) are mere anthropomorphic representations of lesser natural phenomena.
The same applies to the Kami of Shinto religion or equivalents in other "polytheistic" religions. One could easily argue that all "polytheistic" religions are really Animistic religions, which are perfectly compatible with the Atheistic framework depending on how one defines concepts like "Consciousness" or "Soul".
Pantheism and Shamanism as forms of Animism
Pantheism is a simplified version of animism, which removes all "Gods" from the picture except Vishnu (nature). Advaita Vedanta is a form of Hinduism that belongs to this category. Many other religions (eg. Germanic paganism) have a Pantheistic variation, although these advanced forms of religion are rarely known beyond a small esoteric circle of initiates. The Traditionalist School is a school of philosophers from the early 20th century that attempted to explore these esoteric religions and discover a perennial philosophy running throughout all religions. Like Animism, Pantheism is also perfectly compatible with Atheism, again depending on how one defines concepts like "Consciousness" or "Soul".
Shamanism is a variation of animism that involves the notion that the chemical modification of one's consciousness provides access to higher knowledge that is otherwise filtered from our perception. Shamanic practices do not require a belief in any "Gods" and are not uncommon among Atheist intellectuals, especially since the popularization of LSD and Mescaline in the '60s. Aldous Huxley, Ernst Jünger, Alexander Shulgin, Timothy Leary and Terence McKenna are among the more prominent shamans in Western culture, although not all of them would use the term "shamanism" in reference to their chemically induced self-exploratory consciousness expanding sessions.
The link between Shamanism and Hinduism
Much of Hindu belief and practice grew out of the use of Soma, a god, plant, and drink which is the focus of the Rigveda. The continued entheogenic use of drugs such as Cannabis is not uncommon among various Hindu sects. Cannabis is connected with the god Shiva who is said to have rested in the shade of the Cannabis plant on a particularly hot day. In gratitude Shiva gave the plant to mankind. Often the drink Bhang is drunk in Shiva's honor, it is a tea typically cooked with milk, spices, cannabis leaves and flowers. The leaves of the Kratom tree have also been used traditionally as an ingredient in a tea with mild stimulant and opioid properties.
The Pantheistic "God" concept from the Atheist's perspective
The Atheistic naturalistic position of the universe as a very complex quantum computer is pretty much the same as the Pantheistic position of the universe as one highly advanced mind. The differences between Atheist naturalism and Pantheism are really more a matter of different semantics and different cultural bias than a difference in concept.
If one considers the notion that the clock ticks of a computer and awareness are basicly of the same nature (which is a perfectly reasonable consideration), the following statements would mean the exact same thing :
The universe is God. By being a part of God, all matter and living beings are essentially divine. Time is our perception of his thinking process. God's thinking processes comprise of all our thinking processes and all other processes of the universe combined. Our awareness is a tiny fraction of divine awareness.
The universe is a giant computer. By being operating systems somewhat autonomicly operating a part of that computer, all living beings are components of the same computer. Time is our perception of the giant computer sequentially processing information. The computer's sequential processing comprises of all our thinking processes and all other processes in the universe combined. Our awareness is but a tiny fraction of the universe's operating system.
So if time = awareness = clock ticks, I can't distinguish between those two statements. Conceptually they mean exactly the same to me.
In the comment section of an answer somewhere on Philosophy.SE, Swami Vishwananda pointed out there there are some flaws in my description of Hinduism. As I would like to avoid misrepresenting Hinduism, I would ask you kindly if you could please point out any flaws you can find, so I can correct them.