While I personally am for Washington changing their football team name I think your comparison is a little unfair. The logo or mascot you're describing was actually designed in 1971 by a Native American person. The logo was designed with close consultation with Native American leaders, most famously Walter "Blackie" Wetzel, a former President of the National Congress of American Indians and Chairman of the Blackfeet Nation.

Research into the origin of the term "Redskins" suggests it may not have been used exclusively as a derogatory term or racial slur and may have been a term that Native Americans used to describe themselves.

This is from the team website: " In the authoritative linguistic survey “I Am A Red-Skin: The Adoption of a Native American Expression (1769-1826),” Ives Goddard—the senior linguist and curator at the Smithsonian Institution—concluded that the word “redskins” was created by Native Americans, and that it was first used as an inclusive expression of solidarity by multi-tribal delegations who traveled to Washington, D.C. to negotiate national policy towards Native Americans. “The actual origin of the word (redskin) is entirely benign,” Goddard is quoted as saying."

What I've come to realize is all of this is irrelevant though as the general public perception seems to be that the logo and name are offensive. If most people are offended by it, then by definition it's offensive even if it wasn't intended to be.