Sex usually determined one's gender and, therefore, one's work, but the Ojibwe accepted variation. Men who cose to function as women were called ikwekaazo, meaning "one who endeavors to be like a woman. Women who functioned as men were called ininiikaazo, meaning "one who endeavors to be like a man." The French called these people berdaches. Ikwekaazo and ininiikaazo could take spouses of their own sex... The role of ikwekaazo and ininiikaazo in Ojibwe society was believed to be sacred, often because they assumed their roles based on spiritual dreams or visions...Those interested in reading online more about the berdaches might try In Search of the "Berdache": Multiple Genders and Other Myths, or the Wikipedia entry on Two-Spirit.
"I have known several instances of some of their men who, by virtue of some extraordinary dream, had been affected to such a degree as to abandon every custom characteristic of their sex and adopt the dress and manners of the women. They are never ridiculed or despised by the men on account of their new costumes, but are, on the contrary, respected as saints or beings in some degree inspired."
I should add one comment re The Assassination of Hole-in-the-Day, which I have not included in my recommended books category only because it is rather specialized in content and scope, detailing the life and assassination of Bagone-giizhig. It is, however, a scholarly and comprehensive work, recommended for those with an interest in Native American history.
Photo credit. The image is of We'Wha from the Zuni tribe. Another relevant image here (cannot be embedded).