Many sports teams are sensitive to Native American sensitivities and use their imagery and symbolism in a tasteful way.
Many sports teams invoke Native American warrior imagery; however, they do so in a very tasteful way that is not offensive.
Often, regional high school sports teams will invoke Native American imagery and symbolism in a very tasteful way. They do not always have caricatures as mascots. At times they have elegant chiefs and humble spear-wielding warriors. For example, the Florida State Seminoles use an actual Native American on horseback as their mascot. In doing so, they are not propagating any negative stereotypes about the appearance of the Native American people. The mascot has even been approved by the people of the Seminole tribe.
Using any people or ethnicity as a mascot is not acceptable. It objectifies the culture and the people within it. Think about a sports team called the London Chinese, with a Chinese person being their mascot. It doesn’t matter how tasteful the logo or the mascot is, the fact that it is objectifying an ethnicity in this way is offensive. Also, offence is subjective. In the example provided of the Florida State Seminoles, it is true that the members of the Seminole tribe living in Florida approved the use of their people as a mascot for the football team. However, members of the tribe living in Oklahoma have not condoned the use. If even one Native American finds the practice offensive and unacceptable, then it is. It is offensive because it causes offence.
[P1] Native American mascots and imagery can, and is, used tastefully, with the consent and input of tribes. [P2] In these cases it is not offensive. [P3] Therefore, the use of Native American names and imagery in sports is not inherently offensive.
[Rejecting P3] Using a race or ethnicity as a mascot dehumanises and objectifies a people and culture and is always offensive.