Karthik, John, et al, I'm not a PC cop by any means, but I think you're missing the point, and making a legitimate conversation into something ridiculous.
I've never really considered the word "redneck" to be a slur; I typically file it alongside "geek"... terms used with pride by those on the inside, and with derision by those on the outside. Objectively, I'll agree that it is difficult to call it a broadly offensive term, and isn't inherently inappropriate as part of a team name.
That being said, even if you ignore the whole idea of rednecks being poor and uneducated, there are very negative connotations that some associate with the term, far darker than the image of a farmer watching NASCAR. For that reason, for the sake of not alienating potential community support, I believe that 2883 is very wise to reconsider.
The Confederate flag is an appropriate analogy. It is embraced as a symbol of cultural identity by a group of people, its meaning has changed over time, but it is still found by others to be offensive because of its history. Free speech is a wonderful and powerful thing, but I would be reluctant to slap a Confederate flag on my robot... not because I'm worried about hurting feelings, but because I'm concerned about how those hurt feelings would affect my team's bottom line. It's a calculated risk; Jeff Foxworthy has made millions off the term, but it is very legitimate to evaluate if you can reap the same payoff with a high school club, and that consideration shouldn't be raising anyone's hackles.
The discussion on loose usage of the word "Nazi" was discussed
here two years ago, and the points made there are still valid. You aren't responsible for making sure you don't offend anyone, but you do bear the fruit from the offense you cause.
I know you guys are just trolling about offending wranglers, dragons, or people named Fred, but it's really not that hard to tell the difference in the perceptions of "redneck" compared to those terms, and the potential fallout. There are plenty of other places on the Internet for that kind of nonsense.