Difficult, not due to some sort Western cultural superiority, but because the Black Plague and the dark ages in general made things more equitable for women in medieval Europe. It wasn't until the late medieval and the Renaissance that there was a major counter-reaction.
Since a plague might destabilize the Islamic world, that's probably not a viable option for this premise.
Excuse me? Except for literary matters regarding a young and beautiful woman (and that was present in the medieval islamic culture as well, which was much more sensual in that time, by the way), things didn't become equitable for women at all. We can know, for example, that until late in the Rennaisance, the old women were absolutely despised, and there were plenty of poems mocking them as bitterly as possible, for they were deprived from beauty, and hence, what was conceived as their only inherent virtue. And if you're talking about the sexual mores, the Middle Ages were very promiscuous, even if the official discourse was rigid and homophobia was rampant (and it was not nearly as rigid as the Victorian one, by the way). But I can see the point of sexual liberation and women's liberation being close, for when sex stops being an institutional instrument of dominance for both women and the general poplace, things tend to go in that direction.
If you think about it, the three waves of feminism were associated to three fundamental changes in the life of the Western woman.
-In the first one, the liberal ideas started to see convenient for bourgoise women to receive a basic education. The result was that they started to have a wider scope and wonder why they couldn't vote, and as there was no real reason, female suffrage spread and women were legally
emancipated.
-In the second one, as ugly as it sounds, electrodomestic machines spread. That made housewifes to have more free time and share their problems with their female neighbours, so they realized that most of their problems and worryings were common, and started to demand the same oportunities and treatment as men.
-The third one is a result of the success of the second. When women incorporate to the professional world, are able to have total control over their sex lifes, are able to have a fully independent life and start to receive an equal consideration, then the residual stereotypes and attitudes start to look blatantly absurd.
So, in short? If you want sexual liberation to start in the Islamic world befor the Western world reaches it, just make them to develop a scientific method before the West, and make the idea of universal education more commonplace, so feminist ideas can gain momentum. As Islam is not particularily more sexuallly repressive than other religions, and it is by far the most sensualist religion between the mainstream ones, everything else will shortly follow.