The very happy scenario is that Westerners turn their huge force of industriousness they posses, as can be witnessed in the leading role of massive material welfare gains for the last centuries, into spiriutalizing the West (compared to the industrializing of the West that took place.)
This means that Westerners will start a successful spiritual journey on a massive scale. This possibly requires the invention (which is a core aspect of industrializationing) of new ways to be spiritual.
This spirituality must be free of political powerambitions. It respects individuals freedoms and rights, the practice of homosexuality, equal rights for women and treats people of all religions equally.
This spirituality then is the foundation for larger numbers of non-Muslim babies born and attracts Muslims to convert away from Islam to the new spirituality, all over the world.
If one have an idea of how the fabric and actions of a massively spiritualized West would look like, one could tell the feasability if this vision. But who can really say what it would be like? One way to get inspiration for visualizing it would be to take part of the book/audiobook "A New Earth" by Eckhart Tolle. According to my vision based on that book, the society would be peaceful and act from emotional awareness and honesty.
Three other, not as happy scenarios:
There are two when non-Muslims act to ensure that they or their decendants will never live under Sharia law.
One scenario is that the majority of the population declares that a part of their own country will become a Muslim souvereign country and forces Muslims (perhaps that are not both fully westernized and anti-Sharia) to move there. In the remaining of the country, it is made forbidden to practice Islam.
The other scenario may be done if all countries in the world are under Sharia rule, but it is permitted to move to another country. In this case such a large number of non-Muslims may move to the same country that they become in majority and then splitting the country and making the actions as in the first scenario.
Some has speculated that Muslims could be mass-murder in Europe, in the socialist 2000 - th century style (nazism, communism). These first two scenarios may provide roughly the same benefits as the murderous one (I guess) but with less (but none?) violence.
