No statistics, but it definitely has varied over time, depending on just which oppressive regime was enforcing which oppressive dress code. During the reign of the Pahlavi dynasty, the wearing of religious garb by women was banned, creating a significant and very damaging backlash against the regime. Some quotes:
*More problematic was Reza Shah’s unique absolutist approach to changing women’s dress which, following a trip to Turkey, he saw as a hallmark of national modernization. After preliminary steps in 1935, in 1936 women were ordered to unveil and dress in western-style clothing. Some women saw this as the equivalent of going out naked and refused to leave their homes, as gendarmes sometimes tore chadors from women on the streets. According to Houchang Chehabi:
'The forced unveling of Iranian women…was, among all of Reza Shah’s modernization policies, the one that contributed most to his unpopularity among ordinary Iranians. Between January 1936 and the monarch’s abdication in 1941, police and gendarmie used physical force to enforce the ban, thus violating the innermost private sphere of close to half the population…
The practice of limited coeducation for prepubescent children in traditional maktabs was discontinued after girls were forced to go to school unveiled…While educational opportunities improved for women…many girls in observant families were deprived of education, as their parents took them out of school…Reza Shah’s efforts to give both women and men uniform dress codes in line with Western fashions…while meant to unify the nation by eliminating visible class, status, and regional distinctions, in fact deepened another cleavage in Iranian society, i.e., that between westernizers…and the rest of society, which resented the intrusion in their private lives.’*
Later under his son religious garb became the rallying symbol of opposition to the Shah for many young female college students. So:
In the cultural climate of the 1970’s, those opposed to the Shah’s regime increasingly saw as bad everything the regime said was good. Thus, as noted, we find the ironic phenomenon of some women university students from the mid-1970’s on readopting Muslim modes of dress as a means of stressing their identity with Islam, seen as morally and politically superior to the ways of the regime, and/or stressing their political opposition to the regime,whether or not they were believers.
And of course as noted above these royal “reforms” had never really impacted the non-upper and professional middle-classes, such that a large part of Iranian society, especially the pious lower middle-class and the non-urban population had never taken to the new codes at all:
Although women students played and play an important role in political demonstrations and actvities, even more numerous in the demonstrations of 1978 were chadored bazaari women, who came out usually in seperate ranks to participate in the mourning processions, where they had always been, but where their presense took on a new political meaning. As the threat of violence grew, women often bravely marched at the head of processions; participants recognized that this put the police and regime in a difficult position.
The above quotes courtesy of Nikki Keddie’s excellent Modern Iran: Roots and Results of Revolution ( 2003, Yale University ).
Of course the current theocracy is the autocratic bizarro version of the Shah’s autocratic regime in matters of dress. In the current climate I imagine imposed religious attire is considerably less popular, probably pretty strongly against amongst the urban intelligentsia. I would expect it still holds a real appeal amongst the more traditionally pious however, of which more than a few remain in Iran.