I read the links after posting, Ana, not ideal, but it is late.
It is usual for Jewish men and women to be separated for religious and ceremonial events, and there are circumstances when physical contact between men and women is completely forbidden, and would horrify orthodox women as well as men (and ultra-orthodox even more). If the event was very crowded and emotional, there would be a greater likelihood of accidental contact.
That is probably why the women were to be on the opposite side of the road. If the women go along with it, that is up to them. But why not have two notices, one for men, one for women, and why not add "taking part in XXXX"? Or cones marking out a "safe zone" where passing pedestrians (and women) can keep out of the action? The prohibition is as much for men to observe as for women, it is not just for women to keep out of the way of men.