"Though same-sex marriage has been legal in all 50 states since a 2015 U.S. Supreme Court ruling, it remains prohibited on the largest Indian reservation in the country..."

"... which, as a sovereign tribal nation, is not subject to the decision of America’s highest court.... [S]ame-sex couples are at the center of a contentious debate on the Navajo Nation, where the tribal council is weighing legislation to repeal a ban enacted in 2005. The change would grant them equal rights in situations involving property and hospital visitation. Indigenous scholars say it also would honor Navajo tradition, which recognized multiple genders and sexualities that were suppressed and stigmatized after Europeans arrived.... In recent decades, many Native Americans have adopted 'two-spirit' as an umbrella term for 'an individual that has both male and female spirits within them,' signaling a rejection of more rigid, western labels, said professor Gregory D. Smithers.... Two-spirit leaders and activists have made gains, Smithers said...."

From "Same-sex marriage remains banned — for now — in the Navajo Nation" (WaPo).

I was surprised to see that "two-spirit" is not a traditional term. Here's the Wikipedia article on the subject. A short excerpt from what is a long article:

Two-spirit (also known as two spirit or occasionally twospirited) is a modern, pan-Indian umbrella term used by some Indigenous North Americans to describe Native people in their communities who fulfill a traditional third-gender (or other gender-variant) ceremonial and social role in their cultures. 

Coined in 1990 as a primarily ceremonial term, requiring community recognition, in recent years more individuals have taken to self-identifying as two-spirit. Two-spirit, as a term and concept, is neither used nor accepted universally in Native American cultures. Indigenous cultures that have traditional roles for gender-nonconforming people have names in their own, Indigenous languages....

The initial intent in coining the term was to differentiate Indigenous concepts of gender and sexuality from those of non-Native lesbians and gays, and to replace the offensive, anthropological terms that were still in wide use. While two-spirit has been controversial since its adoption, the term has experienced more academic and social acceptance than the term "berdache," which it replaced....

A footnote says that "berdache" means "passive partner in sodomy, boy prostitute."

The binary nature of two-spirit, or the idea of having two spirits in one body, is not a theme found in the traditional gender roles for Native people, and concerns about this misrepresentation have been voiced since the 1990 conference where the term was adopted. Traditional Native Americans asked about the concept rejected the "Western" gender binary implications of the term "Two Spirit," such as implying that Natives believe these individuals are "both male and female."...

The increasing visibility of the two-spirit concept in mainstream culture has been seen as both empowering and as having some undesirable consequences, such as the spread of misinformation about the cultures of Indigenous peoples, pan-Indianism replacing culturally-specific teachings and traditions, and cultural appropriation of Indigenous identities and ceremonial ways by non-Natives....

.... The idea of gender and sexuality variance being universally accepted among Native American/First Nations peoples has become romanticized. Accordingly, the change from berdache to two-spirit is most accurately understood as a non-Native idealization of the social acceptance of gender variance, idealizing a romanticized acceptance of gender variance.[11]...

In academia, there has since 2010 or earlier been a move to "queer the analytics of settler colonialism" and create a "twospirit" critique as part of the general field of queer studies....

The Wikipedia has a long list of traditional Indigenous terms. I'll quote the one that's relevant to the dispute reported in the WaPo article:

Navajo: nádleeh (also given as nádleehi), "One who is transformed" or "one who changes." In traditional Navajo culture, nádleeh are male-bodied individuals described by those in their communities as "effeminate male", or as "half woman, half man."... A Navajo gender spectrum that has been described is that of four genders: feminine woman, masculine woman, feminine man, masculine man.