Specifically, I am curious about how Native Americans managed their relationships to large predators such as Gray Wolves, Grizzly Bears, and Mountain Lions. I understand there is likely variation throughout many tribes; did any tribes hunt and eat these large predators? Did any tribes have an antagonistic relationship with or attitude towards predators? Conversely, did any tribes revere them and consider killing predators taboo?
I live in Montana, and when discussing predator management/hunting, I have heard (totally anecdotally) that some of the Montana tribes consider(ed) it bad juju to kill wolves. I have been unable to find anything to confirm this in my own amateur research. Thank you!
(disclaimer: I am not asking this with an agenda for or against predator killing)
This is a very broad question as it encompasses not only dozens of distinct cultures, but thousands of years of history, too.
The short answer, not surprisingly, is that attitudes varied (and still vary) between tribes and regions. Most of my answer will focus on wolves in the boreal and subarctic, but hopefully this can provide some insight.
In the boreal and subarctic, wolf hunting was common, though most cultures pursued wolves only for fur or to deter predatory attacks on dogs or raiding of food caches.
While Cree and Dene in the Western boreal forest would occasionally consume wolves (typically as a supplemental food source when others were unavailable), The Mi'kmaq, who live in northeastern Canada considered wolves bothersome and hunted them for fur and jewellery only. Likewise, many Inuit in the Eastern Arctic hunted wolves only when they became bothersome and did not consume them.
In the Western Arctic, by contrast, wolves were highly regarded and treated with a religious reverence. Killing a wolf was considered a deeply significant event.
Whaling umiaks (boats) were adorned with wolf skills as talismans and ownership of a wolf pelt was a sign of high status. Hunters would often sleep outside for a period after killing a wolf.
So, there are three broad attitudes across the far North in terms of wolf hunting.
Wolves are treated as any other animal, hunted for fur and occasionally as food;
Wolves are a pest and are ignored except when they are aggressive or a nuisance or;
Wolves are revered and killing one is a significant act.
While I don't have any direct sources regarding attitudes on the Great Plains, Wolves do appear as significant, positive, figures in at least some of these oral traditions.
So, attitudes can vary pretty widely, even among peoples who are essentially neighbours. It would be very difficult to say what the attitude regarding wolves is unless we were able to nail down a specific tribe.
Sources:
Various (1981). Handbook of North American Indians, Volume 6: Subarctic. edn. Edited by Helm J. Washington, DC: Smithsonian Institution
Fogg, B., Howe, N., Pierotti, R. (2015). Relationships Between Indigenous American Peoples and Wolves 1: Wolves as Teachers and Guides. J. of Ethnobiology, 35(2).
Honigmann JJ (1946). Ethnography and Acculturation of the Fort Nelson Slave. New Haven: Yale University Press.