I can't speak to all Native American cultures, so I'll just talk about the Alutiiq culture of the Kodiak archipelago. Before Russian contact and cultural assimilation, there were ample examples of male-male and female-female relationships, as well as multiple-partner relationships. The standard description we have is from Russians disgusted with these practices, so our knowledge is somewhat colored.

Take the description offered by Yuri Lisianskii, who was commanding officer of the Neva on the first Russian circumnavigation of the Earth. As Lisianskii wrote in May 1805:

"Of all the customs of these islanders, the most disgusting is that of men called schoopans living with men and supplying the place of women. These are brought up from their infancy with females and taught all the feminine arts. They even assume the manners and dress of the sex so nearly that a stranger would naturally take them for what they are not. This odious practice was formerly so prevalent that the residence of one of these monsters in a house was considered as fortunate; it is however daily losing ground.

Let's put that into context. From what we know in published sources, the Alutiiq generally recognized (it's important to remember that each region or village might have different customs and attitudes) the phenomenon of a man in a woman's body and a woman in a man's body. Gwenn Miller's Kodiak Kreol, published in 2010, gives a brief description of this with good citations.

The qasguiq was an Alutiiq meeting hall, and contemporary accounts sometimes conflate the name of the hall for the meetings that took place in it. Women were generally excluded from qasguiq discussions, except for those bringing refreshments. As Miller writes, there was one other exception: "The only other women who could attend meetings in the qasgiq were those whose parents brought them up as men with men's names from birth. Their fathers paid a high price for this privilege; they offered substantial gifts to the community leader."

Much of Miller's discussion here comes from Lisianskii and another account written by Gavriil Ivanovich Davydov, who stayed in Kodiak from October 1802 to summer 1803. As Davydov wrote (and here I refer to the Bearne translation published in Arctic Anthropology in 1976):

"Depravity and violent lust are even more widespread amongst this half-savage people: there are men with plaited beards who only do womens' tasks, they live with the women and like them they sometimes have two husbands. Such men are called akhnuohiki. They are not despised, but on the contrary the villagers obey them and they are often wizards. A Koniaga who has an akhnuchik instead of a wife is even considered lucky. A father or mother will consider their son an akhnuohik from the time he is a baby if he seems like a girl to them. Sometimes the parents forecast that they are going to have a daughter, and if they are mistaken they make their son into an akhnuohik.

Lisianskii also writes of an instance where a Russian priest (or monk, the translation is uncertain) was summoned to perform a marriage. The ceremony proceeded as scheduled until an interpreter, walking into the ceremony by chance, "put a stop to the proceedings by making known to the priest that the couple he was joining in wedlock were both males."

Sources also include ample descriptions of polygamous relationships, both with multiple wives and multiple husbands. Take Davydov's account, for example:

"Several women have two husbands each: the first is their actual husband and he chooses the second with the agreement of the wife. The second husband becomes at the same time a kind of servant, that is he carries water, firewood and performs other various tasks. He can sleep with the wife only in the absence of the real husband; when the latter returns he is deprived of this right. Such husbands are nicknamed by the Russians polovinshohiki ["sharers", "half-partners"].

Georg Heinrich von Langsdorff, in a 1803 visit to Kodiak, declared, "No one has given a thought to teaching them morality. Male concubines are more common than in Unalaska." (1993 Limestone Press translation, p. 33)

Now, let's put all this into context. The folks providing these descriptions are very inflexible when it comes to gender roles and identity. They're coming from a very rigid and constrained perspective, and it's understandable if they don't understand them. This is true for sources I mentioned here and that I'm familiar with but haven't used here ─ The Round the World Voyage of Hieromonk Gideon, 1803-1809 and Holmberg's Ethnographic Sketches for example.

Adding to the difficulty is that the Alutiiq would have a natural inclination to conceal facts from people who might look at them with hostility, and the Russians had certainly shown that in the 60 years between first contact and the time that Davydov, Lisianskii and Langsdorff visited. Further add the inevitable translation hurdles and possible mistranslation, and you might understand that we view things through a frosted window.