Those taking offence aren't the group impacted by the names and mascots.
Nine out of ten Native Americans polled said they saw no issue with sports team using their likeness and culture as part of their branding.
Most of the people getting offended by the use of Native American imagery are not Native Americans themselves. Therefore, their offence is not justified. If the people whose culture is being adopted in the branding does not have an issue with it themselves, then the act is not offensive. A Washington Post poll carried out among Native Americans found that nine out of ten Native Americans took no offence from their likeness being used in mascots and the use of their names and imagery being employed in logos.
Even if only ten per cent of the community takes offence to the practice, it is still offensive by definition. If something is offensive, it means that it has caused offense to a demographic or group of people. There is no minimum threshold for offensive. If even one Native American finds the practice offensive, it becomes offensive by definition.
[P1] For something to be offensive, it must cause offence to the demographic or group affected. [P2] Most Native Americans do not find their people's image and names used by sports teams offensive. [P3] Therefore, it is not offensive.
[Rejecting P3] If even one person takes offence, then the object is offensive by definition.