M.R.
I think you would get further with them if you did not classify them with any group of people. Each issue has a solution that has nothing to do with being a red neck or not, so do something about the dog by calling animal control every time you see it out. Call the police or write to your home owners assoicaltion or rental company about the basket ball, swearing, and public nusence they create with the basket ball hoop, lights in your windows, and loud inappropriate langague. You can also contact the police about the noise, though maybe not the content. The rest is just part of living in the city near people. To avoid it, you kind of have to move out to a place where you are in control of your surroudings and no one can live near you.
I think that you should really drop calling them anything but people. It weakens your argument. Some "red necks" are very polite, nice, and care about the people who live near them, and some do not use any profanity at all.
M.