The Iroquois, Cherokee, Navajo, and Lakota are all high-profile tribes who are very used to media attention; I don't think anyone would have the sort of objections one Cree headman with a political agenda had with the inclusion of the Cree. Also worth noting that all four of those are also very aware and very proud of their warrior heritage.
Oh I definitely think as a whole many Cherokee would welcome representation. Particularly since there is a vast spectrum of Cherokee heritage ranging from full tribal membership to casual advocates. And I don't think their representation in a Civ game would attempt to portray them as anything less than competent martially.
HOWEVER, there are some historical tragedies that mainstream media does not like to approach except with extreme, documentary objectivity. The holocaust is one, and why we will never get an Israel civ. The Armenian genocide is another, which is why as much as I want a classical era Armenia that will always have a cloud hanging over its head.
And as far as American history goes, the Trail of Tears is just something that won't be touched. And to be quite honest, I think once enough alt-right videos labelled "Trail of Tears" began inevitably posting on YouTube, pride and pragmatism would be thrown out the window. It would be far more than just one leader complaining about the Cherokee being in Civ.
Also, no one headman or chief "speaks for the Cree," or is mandated or recognized to do so, whatever cultural authority Firaxis saw this individual as having. Each band, who have a name, treaty status, reservation with a townsite, a chief, elders, and elected band council, and allotment of Federal funds, is it's own completely separate unit from all other Cree bands (though they consult each other, and even have meeting of Cree chiefs, there is no one "Cree cultural leader" who speaks with the kind of authority stated). And, as I said, a number of the bands labelled Cree have been disputing THAT ethnic label. Also, some Cree chiefs take pride in the old Cree warrior heritage, rather than denying it even existed, like Matthew Coon Cum, who was even a Grand Chief of the National Assembly of First Nations for a term - and a very confrontational one, or that Chief in Lubicon Lake who briefly declared "independence and secession from Canada" of a chunk of sparsely populated and improved Northern Alberta woodlands, bog, and muskeg.
Mmmmmm. Idunno, I don't exactly have the most faith in people's ability to self-identify heritage, particularly native tribes. And I say this only because we have instances of self-assertion like the Pueblo insisting against historical representation because they believe in some nonsense dark voodoo surrounding replication of sacred imagery and recording of language. I simply do not put blind faith in tribal historiography because the fact is that as a general rule native tribes exist in a sort of limbo between the ignorance of the past and the knowledge of the present.
I mean maybe they have good documentation of being distinct for a substantial period of their history, but I would imagine that there are historians, linguists, and geneticists who could more definitively figure whether a tribe is
actually distinct from the Cree, or if the movement for independence were more a more modern, reactionary trend against selling out to strong, centralized authority.
The fact is that the Cree were aggressively expansionist for a period and maintained a wide trade network. The longer that went on, and the longer any algonquin tribe accepted Cree cultural dominance, the more integrated and "Cree" they would have become: genetically, linguistically, and culturally. At this point Bavaria can't just up and claim that it was never German.
Put another way, the Balkans are a mess of disparate ethnic identities, but for many of them to claim that they weren't "Slavic" would be patently untrue. Or an even clearer analogy, for any smaller Scottish clans--even those which existed in northern England--to suddenly claim that they were never Scottish. In fact this kind of identitarian hair-splitting feels on its face like the inverse of the "no true Scotsman" fallacy.
Obviously there are spectra of identity, and I would wholly believe that there are at least a few tribes who have remained un-Cree-like throughout the years. But absent some hard evidence behind it I would probably err toward the belief that "Cree" is not an inappropriate term for those individuals who a) share cultural signifiers with the Cree and b) speak a Cree dialect.