First of all, the nature of prehistoric animism is speculative. The sentence you quote from the article is focused on ancient organized religions, but I added “in one way or another” to cover animism.

And of course animism is anthropocentric. You’re interpreting it through the lens of mystical monism, so you speak of “interconnectedness,” but that’s hardly the distinguishing feature of animism. You’re mistaking animism for something like Buddhism. See the Cambridge Encyclopedia of Anthropology’s article on animism:

“The person or social group with an ‘animistic’ sensibility attributes sentience—or the quality of being ‘animated’—to a wide range of beings in the world, such as the environment, other persons, animals, plants, spirits, and forces of nature like the ocean, winds, sun, or moon. Some animistic persons or social groups furthermore attribute sentience to things like stones, metals, and minerals or items of technology, such as cars, robots, or computers. Principles of animation and questions of being are thus key to animism.”

Although animists aren’t highly individualistic or dualistic, they nevertheless interpret the rest of the world through the lens of their introspective familiarity with their personhood. Thus their universal principle of animation is mentality, intelligence, consciousness, or “spirit.” That amounts to looking at all of nature as an extension of human nature; hence, human-centered; hence anthropocentric.

Again, “In animistic societies, animals frequently show their sentience, awareness, and motivation to act through their relationships to human beings. Diverse ways of relating to animal sentience are revealed by the ways that hunters and shamans in particular treat animal spirits. Siberian Eveny, for example, consider that the spirits of the animals they hunt in the harsh Arctic climate are master-parents to all humans. As parents, animal spirits may take pity on their children—which include Eveny persons—by offering themselves up as food to eat.”

So that’s a case of animals being treated as extended members of the human family, because of their shared spirituality. Granted, there are genetic relationships between species, but it would surely be cold comfort for the prey of human hunters to be told they’re choosing to die because they recognize humans as their kin. The animals wouldn’t understand any such rationalization because they don’t speak human languages, and that’s because there’s no such close familial relationship. Animals are related to humans physically, biologically, evolutionarily, and ecologically, but to speak of a common spirituality is to anthropomorphize and personify the other creatures.

Notice the contrary doesn’t hold for animists, since they don’t objectify human nature by projecting a stone’s evident physicality onto human beings. No, spirit is fundamental for animists, not lifeless, spiritless, meaningless, amoral, antisocial matter and energy. That’s an asymmetric, human-centered way of looking at nature.

In a sense, animism is less anthropocentric than the later organized religions, because the animists were egalitarian and mythopoeic rather than humanistic individualists. Animists weren’t interested in dominating nature for the glory of our kind. But in another sense, animists were more human-centered precisely because of their metaphysical idealism, their human-centered ontology. The later humanists and theists were dualistic, so they recognized the nonhuman world as something other than us. But the later anthropocentrism lies in their negative evaluation of the rest of the world: nature becomes inferior to us and deserving of being dominated by us. In short, human nature is higher in the Great Chain of being, which is normative anthropocentrism.

(I don’t say the wilderness deserves to be dominated by us or that human progress fulfills a divine plan. I say history is based largely on human disgust towards nature and in pride in our godlike powers, which cause us to attempt to dominate nature.)

You say animism doesn’t contradict modern science, because they investigate the same reality. That’s preposterous. You could say the same about every single way of looking at the world; they’re all attempts to investigate the same one. But you’re confusing the sameness of the referent with the equal value of the systems of representation. The world may be the same, but there are better and worse representations of it, more or less adequate or useful ones.

Animism contradicts philosophical naturalism, because the latter denies magical relations between species and also entails cosmicism which eschews anthropocentrism.

Subjective experience is a valid way of knowing if we’re talking about phenomenology, not ontology or empirical theories of how natural processes work. Animistic myths and traditions are fine records of what it would have been like to have lived in the childhood of our species, as people who were blessedly unaware of the inhuman objectivity of the wider universe and who thus suffered little in the way of alienation.

At their best, as fictions, animism and theism testify to ways of feeling about our position in the world. The myths indeed tell of a mode of experience, not of objective facts. The relevant facts are subjective, having to do with types of mentality and with aesthetic preferences. I’d compare animistic mentality to carefree, childlike naivety, and although that will sound patronizing, I reject the obvious value judgments since I don’t say modern, dualistic egotism is superior. On the contrary, we’re faced with alienation and with an existential burden that may have no satisfying solution.

https://www.anthroencyclopedia.com/entry/animism