Some convention centers were so overcrowded in the ladies rooms the sisters coming out of the stalls had no where to wash their hands because the sinks were all taken up with other sisters who were busy combing their hair or putting on make-up. When a crowded bathroom filled with sisters of all ages and children of all ages became impossibly overcrowded it was necessary at times to cover the mirrors in order to allow those sisters with small children and the older sisters to simply wash their hands.
A simple "Excuse me, I need to wash my hands" might have worked too.
But then again, the brown-paper-covered-mirrors probably cut down on a lot of crazy bathroom catfights.