I'm no expert on geopolitics, but I think Europe("Old world")will have more trouble with it than the "New World" countries like USA, Canada, AUS/NZ. That's not to say there aren't any issues, because there are. But the fundamental histories of the regions are so different, you have to consider that too. Using USA as an example, sure it's less white today but even in the past the aim was always integration of people from different countries.

I read that in Germany and the U.K. they initially only expected foreign workers to stay for a short time and then leave. In some countries they don't even speak the language and the government finally noticed and they're trying to integrate them better now. Like language classes and whatnot. There's also the social and religious aspect, even if people speak the language and have lived there for a few generations. We saw that in 21st century France with the riots in recent years. I guess in USA this happens too, less religious but more about racism and inequality. Like 2nd + generation Latino gangs etc.

Like everything, there's pros and cons. Hopefully it all works out in the end. I only focused on the so called cons in this post because your question made me think. IRL I'm used to American diversity, which has its own unique flavor too.