There are at least two reasons for this.
First, these women were generally fairly well educated at a time when there were not many good jobs available to them. In addition, there were things like labor saving devices that gave them more time away from the needs of their families. Therefore, women were much more able to do things outside the home and work in reform movements (like working in settlement houses) was one of the things that they were allowed to do by social conventions of the time.
Second, many of the goals of the Progressive movement were in tune with middle class values. The Progressives wanted to "clean up" society and make sure that people like the poor and the immigrants were able to live in ways that were more like middle class ways. This sort of goal was attractive to many middle class women, making them willing to work in that movement.