Indulge me in a thought experiment:
The Muslims manage to convert the entire world.
For the sake of this thought experiment, separate the religion from race.
So, everybody is Muslim, but there are white Muslims, brown Muslims, black Muslims, etc.
Everything is pretty much the same as it is right now, in terms of racial demographics, it's just that everybody is Muslim.
So, in the European countries and other Western nations, the majority of politicians are still white, they're just Muslim.
So, what then? Would the world go to Hell in a Handbasket or would things actually get better? Or would things pretty much be the same?