In many new-housing developments, it is in the covenants & restrictions that you can't hang laundry out on clotheslines. It is the most ridiculous thing I have ever heard of, but there it is. It does not contribute to the "upscale" (or, shall I say, faux-upscale) look that developers & builders want to present.
Lynne, I think you should hang out every scrap of laundry you do, in as visible a spot as you can so your neighbors can be "horrified" at it. If they give you a hard time, you can tell them to "show it to me in writing that it's banned." Unless your development has it in the C & R's, in which case that trumps your municipality's ordinances. However, I doubt it, given the age of your neighborhood. I have never owned or sold to a client a home in neighborhoods the age of yours that had such a restriction. My house in PA is in a 30+ year-old neighborhood, about the same age as yours, and there's no such restriction. I could hang laundry out here but our yard is so shady it would never dry....