Most people deny that they believe any racial stereotypes, despite plenty of evidence to the contrary. When we do notice our own stereotyping, it is often because our beliefs are very negative (e.g., believing that African Americans are criminal or Puerto Ricans are lazy). When our stereotypes are "positive" (e.g., Jews as good at business or Asians as smart), we tend to think that these beliefs are not stereotypical and thus not racist.
Sport mascots are based on what is today perceived as "positive" ideas about Native Americans: that they are brave, principled, persevering, good fighters. This "positive cast" to the mascot stereotype leads most to conclude that the mascots are not racist. In fact, it is this "positive cast" to the mascot stereotype that leads many mascot supporters to think that the mascots actually counter racism by "honoring" Native Americans (King, 2002; Sigelman, 1998; Spindel, 2000).
Below: "I'm honoring you, you stupid Indians. Now get out of my face so I can watch Chief Illiniwek."