Sure, but there has to be a question of the reasonableness of those feelings. The term "masticate" sounds dirty, but it isn't. What it seems to me is that the term "red skins" sounds antiquated and passe to the way race is talked about in contemporary times. Consequently, it sounds racist. But I'm not convinced that actually makes it racist.
As far as the N-word, the difference is that there is a long history of the use of the n-word to suppress people. Native Americans were (are) certainly suppressed, but, as far as I can tell, the use of the term "red skins" hasn't really been done to do that.
So I'm fine with forcing Washington to change their name. There are just better arguments for doing so. For example, it's certainly insensitive to name a team after (questionable) characteristics of that race. The word "red skin" certainly fits that. Furthermore, you have to question the validity of naming sports teams after ethnic groups at all*
Personally, if it's OK to name a team after a Native American group I think they should change their name to the Powhatans. That's the major indigenous group to Virginia. Get their permission of course, but use it as a spring board to educate people about Native American culture.
*The counter argument to this is that there are white ethnic sports teams as well. For example, Celtics, Fighting Irish, Trojans, Vikings, etc. However, the difference is that white people are naming the teams after themselves. Teams like Red Skins, Indians, Seminoles are not being named after Native Americans.
Wetback is per se deragatory. The term was created for the sole purpose of being pejorative. "Red" is unpopular contemporaneously, but people are fine with describing people as "white", "black" or "brown". Actually, I think "brown" is super racist because it's a catch all phrase to lump disparate people who don't fit the strictest black, white paradigm into a single group.