What is the Islamic ruling concerning women's participation in organizations, like the Council on American-Islamic Relations)?

Fatwa Question or Essay Title: 
What is the Islamic ruling concerning women's participation in organizations, like CAIR (Council on American-Islamic Relations)?

CAIR is an organization founded to defend Muslims` rights and fend off oppression and injustice that would be inflicted upon them as a result of hate and racial discrimination in this country. These are noble objectives, and participation in realizing these ends by capable people is a good deed that would be rewarded by Allah The Supreme. However, there are some sharia rules that govern participation in them, whether for men or women, and which should be observed, especially for women, such as: Wearing the sharia dress (hijab or head scarf); Avoiding privacy with men and traveling without unmarriageable kin i.e., husband, son, brother, father, etc.; abiding to Islamic code of decorum and manners and avoiding sweet talk.

This participation [in CAIR] should be performed after the woman has done all her home obligations and marital duties and motherly responsibilities. Allah knows best.