I'm Muslim of Moroccan origin. And I can tell you that most people really don't care about Sharia or Secularism. They just want make more money have a good life, education etc.. However I think your idea of progressive is relative. It's not really about the Sharia or the government. It's the people are not yet ready to accept certain progressive ideas. For instance I for my self had no understanding why LGBT are allowed to live until age 26 when I quit Morocco spend few months in Europe moved to US and became recently a proud US citizen. It took me years to question my believes. Met with some LGBT people. Realized they were people like me and you. People are not ready yet for some ideas. It will take years and lots of education. By the way, although I'm a proud american I think Europe is more progressive. US actually is very similar to Muslim countries when it comes to religion. "Westboro Baptist church" for instance.
There are areas and aspects were some Muslim countries showed progressive Ideas. For instance Turkey, Indonesia , Pakistan and Bangladesh all had women prime ministers. The US has yet to elect a woman for president. But these same countries are still backward in concepts like freedom of speech and human rights. So being progressive is a broad term you should really define what progressive ideas you are talking about.