When you have a hammer, every problem looks like a nail. And so liberals believe that the solution to every problem is more socialism. Americans often believe the solution to every problem is more democracy. And Muslims believe that the solution to every problem is Islam. Combine the three, and you arrive at the inevitability of Sharia law in the West. As Muslims harness democratic pluralities in countries that have become socialist and thus less free, they will impose Islamic law.
Even the few exceptions such as Turkey, did not create separate spheres, so much as they imposed forced secularism in order to modernize the country. And these exceptions are also collapsing, notably in Turkey where the Islamists under Erdogan have come to power. The imposed secularism in countries such as Turkey originated at a time when it was thought that a Muslim country had to forcibly secularize in order to enjoy the benefits of a modern state.
But the willingness of Westerners to accommodate Islam, and the billions in oil money that have flowed into Saudi Arabia and the UAE, have discredited that notion by showing that one can be a fanatical Muslim and still be a doctor in England, or own skyscrapers in Dubai, be a Lord or a Peer, a respected professor in a French university or have a nuclear reactor assembled in your country. Political correctness, appeasement and Dhimmitude have eroded the gains made by secularization, and helped radicalize Islam.
Muslim countries who are socially, morally and politically backward, nevertheless have access to all the modern technology and conveniences of the West. Their backwardness makes it all but impossible for them to actually reform their countries so they provide opportunities for their own people, but makes it all too easy for them to export their surplus populations to the West.
And so a goat herder who still believes that he has the right to kill his daughter if she so much as looks at a boy, can get on a 747 and arrive in London or Paris in a matter of hours. New York or Los Angeles in a matter of a few more. His children will go to Western schools, where they will be implicitly or explicitly taught the superiority of Islam, almost as much as they would be in a Madrassa. They will never be forced to choose between Islam and the benefits of the West-- and so they will inevitably choose both, benefiting from their free educations, their professional careers and the good life, while embracing increasingly fanatical Islamic ideas, in order to balance out their materialistic lives.
A believing Muslim, whether Westerners consider him an extremist or a moderate, will believe that Islam and the Koran have the solution for all of society's ills. Social problems are caused by a lack of Islam. In his worldview, Muslim countries can only repair their problems through Islam. And non-Muslim countries in the Dar al Kufr (Realm of the Infidels), Dar Al Harb (Realm of the Sword) are bound to be even worse off, because they don't follow Islamic law. Which means their only solution is Islam.
In such a scenario, Sharia is inevitable. Because as Western liberals think of social reforms in terms of added government control, Muslims think of reform as added clerical control. This makes Muslims and Socialists seem like natural allies, at least for a time, because both confuse reform with centralization that takes individual liberties. Meanwhile the Western Liberal is deluded enough to think that any application of Sharia law will be moderate, when in fact it will be no such thing. Because the Muslim understanding of the world is radically different than the Western understanding of the world.
For example take the recent statement by a Muslim cleric that blames immodestly dressed women for earthquakes. Such an idea has a basis in Islam. It may seem utterly insane to the Western mind, but it demonstrates a worldview in which every individual action is inherently interconnected with the larger social welfare, (an idea shared by both Muslims and Socialists). And if indeed women not wearing a burka cause earthquakes-- then the greater good demands that they be compelled to wear them. After all what is more important, freedom of dress or people dying in earthquakes?
Variations of that argument will accompany resistance to any Islamic ban. And the only response to it can be that the idea behind it is lunatic and unproven. Yet the former would be construed as denigrating Islam and the latter is a useless point, as there is also no way to disprove that (or any other insane linkage that a cleric might come up with).
As a country's population rises, it will approach the Sharia tipping point. Sharia law's imposition will be sold as social reforms, just as they are throughout the Muslim world. And since only disruptive forces would be opposed to it, naturally criticizing its implementation would be one of the first bans. There is only one clean way to avoid it. Just as there is only one clean way to avoid a Communist or Nazi takeover. And that is not to have people inside your borders who want to see the country turn into a Nazi, Communist or Islamist state. If you fail to do that, then sooner or later, you will either face a bloody civil war, or/and live under a Communist, Nazi or Islamist state.