The Western Women not having to cover up is actually a newer concept to SA. Back when US forces were there for Shield and Storm they wanted Service Women to cover up and not drive. We basically said if you don't want Sadam coming across your border you aren't going to stop us.
I remember reading a report that one of our US servicewomen drove a Humvee into some little Saudi town, and when she got out of the driver's seat, one of the
mutaween - Saudi religious police - began screeching at her and approached with a stick to whip her into submission.
She pulled her sidearm and stuck it in the
mutaween's face, which sent him scurrying for cover, much to the delight of other Saudi onlookers. (Seems the
mutaween aren't very popular over there.)
In another instance, a
mutaween somehow made it onto an airbase, and decided to discipline one of the servicewomen guarding our aircraft. He bravely ignored the rifle in her hands and approached her in a threatening manner - and received a burst of 5.56 in the chest.
US forces had her on a plane departing Saudi Arabia in a few hours, and both governments decided not to pursue the matter.