If it is not too much to ask let me please ask that all keep the following in mind when trying to speak to Iraq:
(a) It is not a homogenous society, but divided between Shiite & Sunni, Arab and Kurd, and each has its particular habits and dress.
(b) Given the demographics and sociology of Baghdad, you can count on the following
(i) the majority of celebrators and looters come from the most ‘disfavored’ segements of society, recently urbanized Shiites from the south. Lower education levels, lower income levels, more conservative habits in general than the more urbane and secularized Sunni center. (High level generalizations of course)
(ii) Careful observation will show a marked difference between the Sunni middle class and the shiite underclass. That the women wear the black abayas suggests they are relatively recent urban immigrants, from the country side, and likely to be shiite, by demographics alone.
© in near mob conditions, it is probably wise for women to hang back, above all given the attitudes of the lower rungs of society about mixing. This does not ipso facto hold for middle class and above, indeed often does not, although that has changed in recent years.
Iraq has a long tradition of secularism, that is true – however this was top down secularism, not bottom up secularism. It also, as has been typical historically in the region and outside, been an urban phenomena, so again the recently urbanized have attitudes often at striking contrast with the old urbanites.
However, in recent years, let us say the past two decades, there has been a return to the hijaab (head covering) among Muslims as part of an increasing level of religiousity and ‘fundamentalism’ in a sense of getting back to basics, from their POV. The Niqaab, the face viel, however is usually disfavored by ‘liberated’ but religious women.
Post-war Iraq is going to have to find its own way on these items, and in re womens rights and the like, I would advise letting the Iraqis develop their own idiom on this if one wants to anticipate genuine and sustainable change.
Finally in re Afghanistan, Kaboul is not AFghanistan and outside Kaboul and regions in the north where the Burqa was never really traditional, the Burga remains the rule.