Its the name that is the issue. the logo being associated with it... collateral damage.
The fact that it was drawn by a native american has nothing to do with it really.
If a black artist sketched the profile of an african king and then the NFL chose to slap it on the helmet of a team called the Tar Babies... well, one can see how the association isn't a great one.
At the end of the day, had european settlers taken it upon themselves to live in harmony with native peoples when they got here, rather than massacring them, outlawing their traditions and stealing their lands, using derogitory terms like redskins and savages to describe them, then throwing the original logo on the side of an NFL helmet and calling the team the Chiefs, Warriors, or Americans wouldn't be an issue.