The term 'redneck' is one that I am fond of but I certainly would never consider it racist since, as Jensa says, it has no racial attachments. It originally came from referring to the kind of people who lived in rural areas in Southern America who were more isolated from societed and so held beliefs that could be described as regressive (such as anti-black for example). Since most of these people worked long days in fields, they had burnt necks, hence the term.
Nowadays it is normally used to refer to anyone with these same, regressive beliefs. However, it only takes on a prejudiced meaning if I were to say something like "All those in Texas are rednecks", a stereotype which is widely held. Beyond this, the term is not "racist", if you meant it in this way.
Edit: After checking up on this defintion, I found that it can also be used as a term for lower class people, often Americans (since that is where it originated) often as an insult. Personally, I still don't think this is racist but more do to with class barriers.