When I was in Kurdistan, I heard expats praise certain areas of the Islamic world for being liberal and irreligious. Such areas are good for infidels concerned about safety and the availability of beer, but I can't say I like the idea of relaxed Islam. Catholics are expected to obey Church teaching, and Muslims should be expected to obey the precepts of their faith, so long as those precepts do not violate the moral natural law.
I ate at restaurants in Erbil during Ramadan, which had erected sheets to hide their many Islamic patrons from view. The availability of food during a time of fasting was convenient for me and my fellow expats, but I couldn't help but feel disappointed in the Muslims around us who were blatantly violating the moral teachings of Islam. Erbil is far from the most Westernized place in the Western world. In Turkey, the government actually bans women from wearing a headscarf in public buildings, and bars are common in Istanbul. This secularism is praised by some Western conservatives who also criticize their own societies for being too secular.
We obviously don't want Muslims beheading people for apostasy, but I don't see why we should encourage them to drink beer and wear bikinis. Muslims who aren't into beheadings and bombings could be powerful allies against secular liberalism, but not if they become secular liberals themselves.