I think part of this is related to Western Europeans (people, not the governments) desperately wanting to hold on to the idea (white) US Americans are mostly like George Bush and they (white Europeans) are smarter, more cultured, progressive, and open minded. They see social issues in the US and think they can handle it better. They more widely adopt the ideas of young American activists as their own. They see the US is diverse and think they should be too because if their country is too homogeneous, they are less tolerant and more bigoted than those dumb, racist Americans.

At the government level, Europe is a bit of a mess. A few economies are doing great, but others are still in the pits with little sign of getting better. They're afraid of losing GDP and tax money to help pay for the aging populations and decide the best solution is to allow in more people without a very well thought out plan how they'll make that work out. Otoh, they're still strict about letting skilled immigrants in because many of their citizens are already well educated and there aren't enough skilled jobs for them.

They should realize most of the world isn't going to look at them as racists and intolerant just because their countries are more homogeneous. Most countries are still that way and there is plenty of room in the US, Canada, New Zealand, and Australia for those who want to live in more diverse countries. And if you are trying to create a diverse country, you need to do a better job mixing things up rather than mostly allowing in the most desperate with very different views on things while making it tough as hell for anyone else.

The governments need to find a way to encourage their own citizens to have more children if population decline is such a concern to them. Importing a bunch of less skilled people to pay for the older is short-sighted and in its own way racist.