In the late 19th century and early 20th century, the major European powers conquered most of the Middle East (Egypt, Iraq, etc). They only did a military conquest and didn't try to convert the Muslims to Christianity, but they probably could have accomplished a cultural takeover if they wanted to and didn't decolonize a few decades later. I think that generally, either Christianity or Islam can be dominant depending on which culture is more economically prosperous and has better military technology. In the Middle Ages, the Islamic Empire was more prosperous, and in the 19th century, Europe was more prosperous. In order for a hypothetical Islamic takeover of Europe and elsewhere to occur, the Middle East would need to get on better footing economically.