The book was and is controversial in some places, in part, as pohnpei suggests because of its frank and open references to sexuality among 19th century native tribes. we teach this novel in my history class, and I did have some opposition to it on the school board, although they eventually approved it. In some more conservative religious districts, they argued that the book glorified native religion.
I also ran into an interesting situation where the book wasn't banned, but where they refused to teach it - on the Crow reservation in Montana. Many in the tribe felt the book and the title itself made them look dumb and weak. The Crow tribe has a lot of pride and were offended by James Welch's portrayal of them, even though the book is fiction.
As far as I can tell, the reports that this book was banned are overstated.
Wikipedia claims that "up until just recently, this book was banned in the state of Montana, more so in the public school system." This is clearly not true because no state can simply ban a book and say that no one may read it. Furthermore, the decision on what books are allowed in school systems is generally left to individual districts, not to the state office.
Two more credible sources (see links belows) say that one school district in Montana discussed banning the book. The reason for this is that there were scenes of a sexual nature that were deemed inappropriate for high school students. The attempts did not succeed.