The other examples you give are ridiculous and most assuredly represent your bias in wanting to defend your position.
Most mascots that I can think of are in no conceivable way disparaging towards a specific way a person was born like "redskin."
Some silly example can be given for almost any name, so we need a somewhat stable standard to go by.
I'll present the dictionary. An item universally used to tell us what a word means.
The dictionary says this about "redskin":
Slang, Often Disparaging and Offensive. A North American Indian.
That's not a survey, focus group, statistic, or press release. It doesn't matter the history or intention. If we ruled our society based on things like, "Well it's been that way for a while and we had a good reason to start it," we'd still have slavery.
Other Indian related mascots do not directly address the color of their skin.
Here are the dictionary definitions for related mascots:
Chiefs: the head or ruler of a tribe or clan: an Indian chief.
Braves: a warrior, especially among North American Indian tribes.
Indians: any of the indigenous languages of the American Indians.
I do not understand how this is even an arguable issue. We would never entertain calling a team the "N*gg**s" or "Crackers" or "Slanteyes" because it is a derogatory term related to a way someone was born in which they cannot control.