Women at the 'Azza
The reasons for this have a foot in the present, and not just the past. According to Bahrainis I talked to, there have always been women at the processions. The difference now is the importation of Western-style dating culture, and young people increasingly using it as a flirtation ground, which in Bahraini culture is seen as disrespectful. In other words, the attempts at strict segregation came in response to this modern social development.
There's clearly a sexist element to this, in that it is the women and not the men who have to be behind screens and the one time I saw a man stop a procession to get angry at a mixed crowd he singled out the women and not the men. I suppose the other side of that argument would be that the processions are all male, and obviously can't be the ones hidden. However, this is clearly a situation in which social reality is more complicated than it first appears.