I'd argue that, under some conditions (e.g. Iran's conditions now), the fight against sexism (or against religious obscurantism) needs to be subordinated to higher priorities. The ranking of priorities in the struggle is not dictated by the left (inside or outside), but by the dynamics of each particular society. (Julio Huato, "New Spirit of Capitalism," 9 October 2007)If we look back in history, we can indeed see how the empire has sought to exploit divisions in its target nations, including the gender division, and sometimes succeeded in doing so. The roles that Poder Feminino and other women's organizations, such as wives of striking copper miners in 1971 and those of striking transportation workers in 1973, some knowingly, others unknowingly, played in destabilizing the Allende administration are the best known example. In the case of Chile, the most powerful component of anti-government women were religious conservative upper-middle-class women; in the case of Iran, secular liberal upper-middle-class women are among those whom the empire wants to use through its "democracy assistance" component of the regime change campaign.
The best response that Iran's government can make to the empire's "democracy assistance" is to reform Iran preemptively, strengthening women's rights, expanding sexual freedom, and so on, but both the government and society it governs are made up of people who have a wide range of opinions about these questions, and some sectors of the population are even more conservative than the government itself, so no change can come about overnight.
In the meantime, therefore, we ought to concentrate on getting Washington to take regime change off the table, so people of Iran can concentrate on reforming the state and society without worrying about social conflicts being exploited by the empire to create a climate of ungovernability and impose its imperial solution.