Scott Sumner notes that the USA's demographic profile in 2060, which some people on the right are worried about, looks quite a bit like Texas's profile today:
Neoreactionaries seem to think the America of 2060 will be a particularly inhospitable place for white people. And yet white folks are moving to Texas in droves. Indeed the only other state that comes close (in terms of absolute population growth) is Florida, which also has lots of blacks and Hispanics (but not very many Asians). The Texas economy is also highly successful. Even during the oil bust, people continue to move to Texas and its population continues to grow rapidly, up by nearly a half million (almost 2%) in the most recent year (mid-2014 to mid-2015). The unemployment rate is only 4.2%, close to the 4.0% considered optimal by Bernie Sanders. And this was accomplished despite the hemorrhaging of oil jobs.
In the UK, some people are worried about the number of Muslims. Pew Research reckons that by 2050 about 11% of the population will be Muslim, which is about double what it is today. London is about 13% Muslim, and it's among the best cities in the world. There isn't any major civil unrest, though Tower Hamlets (which is 30% Muslim) has had some pretty serious problems with its politics.
Those Muslims aren't evenly distributed around the country, though: about 40% of England's Muslims live in London and the others are mostly in cities like Bradford, Birmingham and Luton. Perhaps if London's Muslim share of population doubled it would be quite a bit different to how it is now, which people might not want.
This is mostly driven by birth rates, not by immigration – there isn't actually a large amount of permanent Muslim immigration to the UK anymore. It seems like people concerned about this should want more, not less, immigration from places like Eastern Europe.