Islam does a good job keeping women under control and making them do their civic duty towards humanity (namely, having kids). If they get nothing else right, that alone will keep them growing.Eventually, Civilization will stagnate.
I'll imagine it'll look like the Game of Thrones universe, sort of.
With Muslim families scheming for the throne.
I read a book authored by two economists who had accurately predicted bad markets and economic situations in the Seventies and Eighties. According to these economists, the United States could eventually evolve into a city-state structure. Imagine the Chicago Alliance (a name I just conjured up), an economic alliance between Chicago, Milwaukee, Madison, and a host of smaller cities in Wisconsin, Illinois, and Indiana, possibly extending into Michigan. City States and alliances would form across the United States. These City-States would be independent of a central government. Each has its own structure, security, and taxes. Other regions across North America could adopt this decentralized government model, as they pledge allegiance to a City State for protection.
We are so divided now that I could see that happening in the future. Not in the near future, but long term. Imagine if Blue regions split from Red regions. When you look at a voting map, blue regions are urban areas with higher populations. Red areas form an economic and political alliance to counter the Blue. But, the Red areas control a lot of the resources. So Blue Chicago City State makes an alliance with the Red areas, forming the Chicago Alliance. But the alliances are not fixed so loyalties could shift and form partnerships with say, the Minneapolis City State.
The economists factored in religion, but this was before the great Muslim immigration to the United States. Kinda does sound like the Game of Thrones, minus dragons and witches.