Religion is Interpretation...nothing more ! So FACT 1 may not be that certain...when the Quran talks about women covering themselves up and Muslim men lowering their gaze...one might interpret that in various ways. The women in my family use only, what we call in the Subcontinent, a 'Dupatta' to cover themselves up...if need be, for that is their interpretation of that. However other more, what I'd call, stringent interpretations do exist and unless they pose a serious security threat then let them wear whatever they think conforms to their understanding of religion !