In Iraq, it is interesting to notice that Saddam Hussein regime was totally non religious. It is only since he is not in power any more that there has been so much religion poured in the Iraqui society, with its consequences, as women wearing scarves, and sometimes completley covered. The Baas party which Saddam Hussein belonged too was non-religious, the creators of the party were chistians and muslims. The Baas was nationalist, and pan-arabic, but definitely not religious.
During the first years of Saddam Hussein regime in the 1970's, the regime pushed for industrialization and economic development of the country, and education for all, and gave equal rights to women. In 1973, school became mandoatory, free and non religious for boys and girls. In 1977, 70% of pharmacists and 46% of dentists were women.
Then since the 1980's, he turend into a dictator, killing massively ethnic minorities (especially the Kurds) and potltical opponents. Don't forget Saddam Hussein was supported by western powers in the Iran - Iraq war 1980 - 1988.
Iraaq is far from being the worst place for women. Iran since the islamic revolution in 1979 is a lot worse.