As far as Islamic Shari`ah is concerned, there is nothing wrong in a woman taking over the leadership of administrative and financial affairs and necessities of a mosque or to be a director of an Islamic Center. As for a menstruating woman attending the mosque, this is a controversial issue among Muslim jurists and the most correct opinion is that it is permissible as there is no authentic text to forbid menstruating women from attending the mosque and most mosques today have offices and adjacent rooms other than the prayer hall.
Sheikh Mohamed El-Moctar El-Shinqiti, director of the Islamic Center of South Plains, Lubbock, Texas, the US, stated: There is no impediment for a woman to be a president of the mosque, i.e. to take over the leadership of administrative and financial affairs and other mosque necessities. Many Muslim women in the past built mosques as part of the Islamic waqf (Arabic for: endowment) system, and they used to have the final say in choosing imams, teachers, and other employees of the mosque, as well as handling the mosque’s finances. This is similar to what any director of an Islamic center in North America does nowadays.
As for menstruating women entering the mosque, it is a controversial issue in Islamic jurisprudence. The Hanbali School, for example, do not see a problem with women attending the mosque while in their cycle. Some of those who opposed to women entering the mosque during menstruation based their argument on the fear of contaminating the mosque, which is easy to avoid nowadays.
In general, there is no authentic text to forbid menstruating women from attending the mosque. But the hadith encouraging menstruating women to attend the `Eid Prayers, states that they should avoid the Prayer area.
Anyway, most of the masajid (Arabic for: mosques) today, especially those in Western countries, have offices and halls outside the prayer area.