I'm surprised no one else has commented on this. The practice of avoiding women during their menstrual cycle - or women being secluded from their communities during this period - is very common in cultures not only in the Americas, but all over the world. For a long time, anthropologists associated this with "pollution" or a "taboo" regarding menstruation, but in the 1970s others began arguing that this might have implied a certain reverence for women's spiritual power.

As anthropologist Thomas Buckley wrote in Blood Magic (1988):

The "menstrual taboo" as such does not exist. Rather, what is found in close cross-cultural study is a wide range of distinct rules for conduct regarding menstruation that bespeak quite different, even opposite, purposes and meanings. Many menstrual taboos, rather than protecting society from a universally ascribed feminine evil, explicitly protect the perceived creative spirituality of menstruous women from the influence of others in a more neutral state, as well as protecting the latter in turn from the potent, positive spiritual force ascribed to such women.

There are numerous colonial accounts of such practices among Native Americans, bearing in mind that the descriptions were colored by the bias of the authors.

• For example, French explorer Pierre Liette wrote of the Illinois in 1702 that they had a small hut near each cabin built for menstrual seclusion, "to which they retire with a kettle, a spoon, and a dish during all the time they are in this conditions. No one enters save those who are in the same condition. When they need anything they come to the door and ask for it." During their first time menstruating, they built a cabin about a half mile from the villages and were told to abstain from eating and drinking during their period, since "they see the spirit [manitou], and that when he has spoken to them they are everlastingly fortunate and achieve the gift of great power for the future." One girl had spent six days in the hut without eating, and (according to Liette), "she had made all her relatives believe that she had seen a buffalo, which had spoken to her, and that her two brothers who were leading a war party against the Iroquois would make a successful attack without losing anyone. They did indeed make a successful attack, as she had said, but one of the two brothers was killed. All the medicine men said she had been right, because the attack had succeeded, but that apparently she had not fasted long enough."

• Jesuit Gabriel Sagard, in 1632, reported that Huron women were separated from their villages during their menstrual cycle and were forbidden from having contact with men. They also had separate pots for cooking their own food.

• Missionary David Zeisberger reported that among the Delaware, women also lived in a small hut during their menstruation, and during this period "they are not permitted to do any cooking or domestic work. None will eat what a woman in this condition prepares, for food prepared under such circumstances is said to be unwholesome and to cause pain in the abdomen."

• Father Crestien Le Clercq reported that among the Mi'kmaq, women and girls who were menstruating "are accounted unclean. At that time they are not permitted to eat with the others, but they must have a separate kettle, and live by themselves. The girls are not allowed, during that time, to eat any beaver, and those who eat of it are reputed bad; for the Indians are convinced, they say, that the beaver, which has sense, would no longer allow itself to be taken by the Indians if it had been eaten by their unclean daughters."

• The Sieur de Dièreville also reported of the Mi'kmaq that men who came into contact with women during her menstrual cycle would love the use of their limbs, and if "she were to touch his musket during that period, he would believe that it was bewitched, & that he would be unable to kill anything with it; so strongly is he possessed by this idea, that he fears less the most malign spells of the Magicians."

So it's clear that women were considered to be in a spiritually charged state while they were menstruating, but this could have different consequences - it may have led to avoidance as much as reverence in many cases.