As with many aspects of New Age and alternative wellness belief systems, it seems like this obsession goes back to the 19th century. In the late 19th century, North America experienced the rise of many alternative health and wellness movements, as well as spiritual movements. Many of these are direct ancestors of the New Age. There’s New Thought, which is basically the same thing as The Secret; Theosophy, which imported exoticized versions of Eastern religions into the West; and medicine shows, in which people selling all sorts of health remedies toured the country and put on shows to impress potential customers (incuding the infamous snake oil salesmen).

At the same time, anthropology emerged as a form of study of human lives and societies. According to historian Philip Jenkins’s book about the American settler relationship to Indigenous spiritualities, this mainstreamed some vague knowledge about Native American ceremonies and beliefs, and normalized them as an object of study or fascination (as opposed to earlier assumptions that they were superstitious or dangerous). He ties this to the strengthening of a stereotype of “noble savages”, which stereotyped Indigenous people as uncorrupted by the ills of civilization and industrialization, and thus a lot more spiritual and in touch with nature than mainstream American culture. Works by these anthropologists also made elements of Indigenous spirituality accessible to Americans through books, as did travellers’ accounts of people visiting Indigenous communities and reporting back in an exoticized tone.

So, for aspiring medicine show sellers, tapping into this image of an undespoiled culture that knew a lot about nature could be lucrative. Although other cultures were also appropriated for this purpose, it became pretty popular to sell cure-alls or fake remedies named after Indigenous cultures (even if the actual recipes had nothing to do with Indigenous people).Ferris State University’s article about anti-Indigenous stereotypes lists a few examples of these pretendian medicine show products: Kickapoo Indian Salve, Big Chief Liniment, and Indian Stomach Bitters. Jenkins cites this as a cultural influence that put the idea of ancient Native healing secrets into the American consciousness.

By the end of the century, this image of Indigenous people as possessing ancient secrets and a unique connection to nature passed into American fine art and literature. Western artists and tourists frequently visited Southwestern Indigenous communities like the Hopi for events like the snake dance, and integrated their impressions into their art. Poets like George Cronyn extolled the naturalness and simplicity of Indigenous life, and a collective of artists called the Taos Society based themselves in Pueblo territory and used Pueblo, Hopi and Navajo motifs, among other notable poets and members of the Arts and Crafts movement. The appeal of these Native motifs were strongly based on the idea that Indigenous spirituality was special: for instance, writer Mary Austin claimed to have been forever changed by an experience with a Paiute medicine man, writing that she thought she coming back to “an uncorrupted strain of ancestral primitivism” (Jenkins, 77). Their work injected this idea of a pure natural form of spirituality and healing into the white American imagination, and made it sound intellectual and respectable rather than scary or superstitious. They juxtaposed Native spirituality to Christianity, which they constructed as puritan, over-intellectualized, and affected. However, their image of nature-based spirituality remained vague, and they mostly described it in contrast to Christianity rather than on its own terms; rather than describing Native beliefs, they refracted them through their own lens and used the artistic motifs or music or ceremonies for their own needs.

This is probably sounding familiar for anyone who knows about the New Age. The key move here is that white Americans interested in Indigenous spirituality took the specificity out of it and extracted beliefs about the importance of nature or the oneness of the universe, which brings us to the most direct ancestors of the New Age, which flourished during the First World War and Great Depression. For instance, Theosophy was based on the idea that all spiritual systems lead to a similar kind of enlightenment, and mix and matched from Western occult systems, Jewish Kabbala, Hinduism, Buddhism, and global Indigenous ceremonies. This system was founded by Helena P. Blavatsky, a Russian-American woman who claimed to have unique insights into human origins and the oneness of all spiritualities. She became a sensation amongst the middle class of the English-speaking world, the same kind of audience as the artists described above. She wrote that Native pictographs were actually an ancient system of writing that came from Atlantis, that the Serpent Mound of the American West was a sign of a universal religion that also included Hindu snake worship, and that there was a whole lost history in which Native Americans had been connected to the same ancient universal religion as the Norse, the writers of the Vedas, and other ancient cultures. In Spiritualism, a kind of working-class counterpart of Theosophy, mediums who claimed to be able to talk to the spirits of the deceased often claimed to have been taught by Native Americans.

Since these systems and ideas were the inspiration for so much of the New Age (a universality amongst all religions that can be perceived by the enlightened, the appeal of ancient secret knowledge, a vague reverence towards nature, and distaste of hierarchical religions), we can argue that medicine shows, turn-of-the-century artistic transcendentalist influences, and spiritual systems like Theosophy imparted New Age’s fascination with Indigenous spirituality.Ultimately it all comes back to the trope of the noble savage, the idea that Native Americans are especially undespoiled by modernity and innately spiritual.

What you are referring to is likely a concept known as "Plastic Shaman." But first some background:

The New Age movement first arose in the 1960s and developed rapidly throughout the 1970s and 1980s. Its haphazard and varying belief systems are hard to quantify as they vary from person to person, but generally speaking, it is a religious movement based on unifying the mind, body and spirit. Typical practitioners are of middle to upper-class backgrounds and because there is no central authority that constitutes what isn't or is "New Age," it remains a highly controversial topic.

Generally speaking, the New Age movement is a response to the social isolation felt by white, affluent and suburban middle-aged baby boomers who feel disconnected from cultural traditions, spiritual meaning and community belonging due to the effects of late consumer capitalism (1). The New Age Movement can be seen as one response to the decline of traditional religion in the West. Practitioners see the world's various spiritual traditions as public property and are thus no longer subject to traditional social rules that forbid their use by religious elites and other cultural qualifiers. The sacred becomes commodified due to the degradation of sociocultural boundaries and thus the general argument allows that it can be bought and sold and thus consumed according to basic free-market principles (2). However, as products of the very consumer culture they claim to reject, they seek to pursue spiritual meaning and cultural identification through means of purchase. Ultimately, this search for meaning through material acquisition leaves them unsatisfied as the community they gravitate towards is 2-dimensional, built on the promise of advertised products with no underlying histories or social relations which would fulfil that need for a real sense of belonging. Thus New Age practitioners not only mask the social oppression of Native Americans but also perpetuates this oppression (1). Furthermore, indigenous culture is often in direct conflict with the idea of commodification whereas the western notion of intellectual property is market-based, thus complicating legal protections to indigenous spiritual identity (3).

The term plastic shaman or plastic medicine people refer to individuals from this movement that attempt to pass themselves off as shamans, holy people, or spiritual leaders without genuine connections to the culture that they claim to represent or their connection is seen as disingenuous and exploitative for ego, power or money (3). The majority of these plastic shamans, typically Americans of white European heritage, find their consumer niche largely in the publishing industry where alternative medicine and cures are big sellers, after all, membership in a New Age cult is often largely defined by participation in consumption (1). These people are trying to fill a void which modern medicine and culture cannot "cure" and are addressing symptoms rather than causes.

Often consumers of the products from these New Age gurus are insufficiently familiar with individual Native American religions and cannot distinguish between imitations and actual traditional practices and customs (4). Practitioners are generally more interested in the aesthetics and iconography of romanticised indigenous practices, rather than the indigenous peoples themselves and the social, political and economic challenges they face or the history behind these practices. Typically, plastic shamans sell experiences under the guise of "innocent yearning," hiding their very real complicity with the domination of indigenous culture (1).

This misrepresentation of indigenous culture is seen as an exploitative form of colonialism and part of the continuing trend of neutering and destroying indigenous cultural heritage. By removing the cultural connections from these items, Plastic Shamans create microcosms of neocolonialism, implying that the indigenous themselves are incapable of sharing their knowledge, wisdom and history with the rest of the world. This practice reinforces the idea of the noble savage, denying the humanity of indigenous peoples (5). Defenders of indigenous cultures have thus coined the term to criticise people who are potentially harmful and dangerous to the legacy of these cultures and the communities they claim to represent (6). Practitioners of these practices often use "freedom of speech" as a defence against critics, however, the abundance of these consumer goods often ensures that native voices will never be heard (7). This affects both their ability to represent their culture and advocate for better material conditions long term.

So what is the draw to Native Americans in particular? I would argue that indigenous culture is specifically targeted due to the lack of legal protection and its immediate availability. An already disenfranchised cultural group already has little means to defend itself especially when courts have been historically reluctant to provide relief when their rites are appropriated and have a long history of being denied basic affordances of dignity (Examples of these cases can be found in ref (3)). Indigenous culture already had a long-established history in popular culture as a motif of "the Other" to whom prevailing cultural sentiments, anxieties, propaganda and political moods have been projected. Often these historical characterised depictions of native peoples represented non-native desires, rather than indigenous lives or cultures. This almost "tabula rasa" of a cultural package offered a quick and easy aesthetic for plastic shamans to adopt and monetize under the guise of spirituality. It is a manifestation of the idea of the "Noble Savage" which offered a fantasy alternative to modern life for Europeans and Americans (1).