Culture of Egypt is a blend of rare combo of conservative and friendly attitude. Where the safety of women is society is concerned, people put high value on virginity and pay respect restricted and restrained approach from women in return.
Apart from locales, in terms of safety of foreign women traveling alone, Egypt is a completely safe place. People of Egypt are generally helpful and in case of any sort of problem women may contact local police or may ask for help from common shopkeepers also. However, it is always safe to wear conservative dresses on Egyptian roads because Egyptians respect conservative approach from women in general. Before planning for Egypt trip one should read and get some real life information about Egyptian culture & tradition, women are no exception from this unsaid safety protocol to enjoy a hassle free Egyptian holiday time.
One more line of caution: in order to remain safe in Egypt for women traveling alone, should remain indifferent to local incidents or disputes if any, and should check the date of holidays beforehand. It is not safe to visit Egyptian remote tourist spots alone or on off days.