I am living in Cairo at the moment and the advice we women are given on arrival is: If you don't want problems, cover up. What we tend to do is keep a light shirt in the car and put it on when you are outside. It is no big deal. I think you have to remember where you are and that customs are different from at home.
We were also told that you don't really have to cover up to the same extent in the Red Sea resorts so I am a bit surprised to read about this.

cheers,
Margaret