My Great Grandmother was 3/4 Cherokee. I personally don't find it offensive that my ancestors are the model for a team mascot.

It doesn’t hurt me, though I’ll readily admit that meeting me you’d never know I have Native American heritage.

I personally don’t think that’s how people see Native Americans. Unfortunately, I think a lot of whites have a view of Natives as alcoholics that don’t do much except gripe about what they lost (not my view, but a widespread one). Alcoholism is actually a huge problem within the native community and I should think time and resources that are being devoted to the school mascot issue would be better spent on more serious matters. Diabetes is an enormous problem that's killing tribal members in huge numbers every year. I think it’s much more important to focus efforts on life saving and life altering causes rather than cry about a tomahawk wielding “Indian” on the jerseys of the local high school’s team.

In one of our neighboring towns the team mascot was a coon. They were the Frisco Fighting Coons. Now, these weren’t the “coons” you may be thinking of; it’s short for racoons. They are little furry creatures, and they were the furry “Coons” for nearly 80 years. In March of 2002 they changed the name to the Raccoons. Not a big deal really. It was a pretty easy transition, but there were still people who hated that the tradition changed.

From the Amarillo Globe-News:

FRISCO (AP) - The Frisco Fighting Coons are no more.
1. Some students and parents in the North Dallas suburb had complained the nickname was racially offensive, and the Frisco School Board agreed Monday night, voting unanimously to change the nickname from Coons to Raccoons.
Superintendent Rick Reedy recommended the change.
Of several dozen people at Monday night's board meeting, many were vocal in their desire to keep the nickname the same as its been for 78 years. Some wore T-shirts and had signs in their yards reading, "Don't Rac my Coons."
Supporters said they had never learned to use "coon" as a racial slur and were proud of the nickname, created in 1924 when no one attached any racial significance to the name.

I don't know the answer, except that you can't pease all of the people all of the time.