Native American folklore isn't my area, but I can say that many Native American groups had traditions involving skin changing. And they shared this tradition internationally (not to suggest that these diverse traditions are historically linked). They were taken very seriously and they were a form of folklore (I don't understand your use of "taken seriously" or "just...folklore": folklore was and is taken very seriously by people who believe the traditions).

The following is an excerpt from my draft "Introduction to Folklore"; it steps in midstream after a discussion of the nightmare (another form of skin changer - of a sort) and makes references to other parts of the manuscript, but you should get the point - this being a means to open the door to the European-equivalent traditions, and by analogy, this being a means to understand other cultures that include the concept of skin changing:

The werewolf was the male counterpart of the nightmare. While this cursed man sleeps, his spirit travels the land in the shape of a wolf. Unlike the nightmare, who merely gave bad dreams, the werewolf kills livestock and people, having a particular affinity for pregnant women. Like the nightmare, the man sleeps unaware that his soul prowls the land in animal form. His identity is discovered when he is wounded in wolf form or someone calls out his name. Werewolf stories can conclude with the disenchantment of the man, but some also end with his death.

The idea of the werewolf draws on a much older tradition of shape shifting. There is clear evidence of a widespread European tradition that people, and men in particular, intentionally took animal forms through magical means or special talent. This belief appears in the Satyricon, the first-century Roman work of Petronius, described above. In this story, a soldier who is a versipellis, a skin-changer or werewolf, is walking among some tombstones one night when he removes his clothes and urinates around them. The clothes turn to stone, and the soldier becomes a wolf. That night a wolf kills some sheep, but the slave tending the animals pierces the wolf in the neck. The next day, the soldier, in human form, is found to have a wound in his neck.

Reidar Th. Christiansen classifies stories of this kind as Migratory Legend 4005, in which a man’s wife discovers that her husband is a werewolf as indicated by wounds that he has received. The act of recognition releases the man from the spell. Ella Odstedt in her Varulven i Svensk Folktradition (1943) describes three principal ways in which a man becomes a wolf: the man is mother had magically avoided pain in childbirth, and this brought a curse on her child; a curse is magically placed on a man by another person; or the werewolf actively and magically brings about his own transformation. Odstedt suggests that the last of these causes is the oldest. Dag Strömbäck supports this suggestion. He further points out in his Folklore och Filologi (1970) that Old Norse sources confirm the idea that men magically caused their own change.

Icelandic sagas give considerable details about men who caused their own transformations into wolves and bears; ulfheđin and berserkr, respectively. These terms, which literally mean “wolf coats” and “bear shirts,” refer to the belief that men could either cause their actual transformation or that they could magically acquire the attributes of the ferocious animals by wearing their skin and going into a trance. Such men were feared in battle because they believed that neither fire nor steel could harm them. According to tradition, these men thought themselves to be invincible, and so they charged into battle recklessly. Most of Scandinavia outlawed the practice of going “berserk” because people regarded these men as dangerous, destructive, and generally anti-social. The sagas describe heroes who confront groups of these men and defeat them with great difficulty. Whether or not these literary accounts and records of laws indicate that some men actually believed they could transform themselves is a matter of dispute. Accounts of witches and laws against witchcraft does not mean that there were witches. On the other hand, there were certainly people who felt they could use magic for a variety of purposes. By analogy, there may have been men who felt they had the power to transform into bears or wolves.

Odstedt and Strömbäck identify the oldest elements of the werewolf complex, and they demonstrate the antiquity of these elements. The story of the versipellis in the Satyricon is a still older manifestation of this belief. The soldier of the legend actively causes his own transformation, and this supports the contention that intentional transformation is the oldest tradition. There is evidence that Marie de France, a twelfth-century author from the nobility, helped spread the idea of the cursed werewolf who cannot control his own magical change. She wrote a widely-distributed story containing this motif. Because of the power of the written word in folk tradition, Marie de France may have had a role in changing the story as popularly told, making the werewolf the victim of magic as her version ascended in importance over the older tradition of a man intentionally changing himself.

This is not my area of expertise, but to echo /u/Reedstilt, skinwalkers are still very prevalent in Navajo/Dine culture, and have seeped into the greater Hispanic and Anglo folklore/mythology in the U.S. Southwest. In my conversations with Dine friends, they do not discuss skinwalkers with outsiders except in the most vague terms, and even in the urban centers of the region there is still a lot of fear of skinwalkers. Any dismissive comments that they are "just a myth" will be met with serious concern and assurances that they are a very real aspect of Dine culture. Hispanic and Anglo decent New Mexicans also have their own experiences with skinwalkers, and though the cultural constraints on discussing their existence are relaxed, the fear is still present for many who grew up near the Navajo Nation.

For clarity's sake, skin-walking is a very particular subset of animal-transformations. Skinwalkers proper are Navajo-specific and are always bad news to put it mildly. The things a person must do to gain such powers demonstrates that moral restraint isn't one of their stronger attributes.

Now animal transformations as a generic supernatural ability is found over a much broader area, and the person whose able to do such things isn't necessarily Always Chaotic Evil like the skinwalker.

So are you asking about skinwalkers specifically, or animal transformations more broadly?

If you are interested there are also the stories of the Nagual of Mesoamerica. They are not universally viewed as evil like the Navaho skinwalkers are.

In the tales I'm familiar with, they tend to be women (though they can be men) and serve as sort of a similar role as a witch women in medieval Europe. I've heard some stories though where people talk wondering how much is the native myth and how much is the Spanish transposing the European witch on top. But there are a lot Brothers Grimm morality type tales associated with them. And there is also a lot of tales of them protecting "native traditions" even in some small way against European domination.

It's hard to find good sources in English for them though. The better sources are in Spanish.