oh right, this isn't offensive, looks like a friggn angry Japanese kabuki actor
Ask the native Seminoles, not me. Their privilege, not mine or yours. When the Seminoles no longer want that image they'll say so. Their heritage, not mine.
But the problem for the Washington Redskins team is that Native American peoples all over the US object to the term redskin. There was a similar conflict with continued use of the term "Fighting Sioux" for the University of North Dakota (UND) teams, especially their top-ranked hockey program, using a logo very similar to the one you post here.
Among the issues were the word Sioux itself, not truly a native term. Early French fur trappers had altered & shortened a longer native word, used more commonly near Ottawa by the Ojibwa. But in the Dakotas the preferred native words were Dakota, and Lakota. Think of the movie Dances With Wolves
Nor do many "Sioux" feel comfortable with their portrayal as "fighting." They were actually relatively peaceful tribes, not perpetually warlike, and only fought as the need arose. I spent time at their reservation schools, encouraging them to come to UND. Lovely & generous people, nothing like the negative Indian stereotypes from the movie Westerns.
And BTW, North Dakota voters ended the Fighting Sioux name & logo in 2012. A new school sports logo cannot be chosen until 2015. So there is precedent for this, though at the college level.