The Seminole Tribe is very PRO their name being used as the FSU nickname. The Tribe actually petitioned the NCAA to allow the name to remain, and the NCAA agreed.
In contrast, the derogatory term "red skins" is decried by pretty much all Native Americans (and most other people).
The OP on the subject wasn't commenting on the Seminole nickname, rather the Tomahawk Chop. I think the baseball Braves do something similar and I agree with the OP that I find it strange that no one seems to object much to something that - at least on the face of it - looks objectionable. Likewise, while everyone is decrying the Redskins, compare the Native American in their symbol to the caricature of the Cleveland Indians symbol - another not-so-publicly objected to symbol that I don't get why not.
While I don't disagree that enough folks dislike the Redskins name that it ought to be changed, the Native American community is by no means in 100% agreement as to it being objectionable. Although I think that some who don't find the term itself objectionable, probably depends on the situation. My biggest issue with these name changes isn't that I want to see folks feel insulted, but that names of various teams were changed (such as the St. John's redmen) whereby the name had absolutely nothing to do with native Americans.