How should the centre left in America and Europe deal with immigration?

So as we all know immigration is becoming a massive issue in elections in America and Europe, and far right parties are winning on platforms of reducing Immigration, especially immigration from non white countries.

Trump rode into power on a platform of mass deportation. He's declared an invasion at the Southern border and is sending troops to the Southern border. And immigration and trans issues are the only two issues where Trump is polling positively.

Europe, even Western European countries are experiencing a surge of far right parties on the explicit promise of cracking down on immigration. The PVV won in the Netherlands in 2023, the far right in France is growing more popular by the minute, they did pretty well in the legislative elections last year. Reform UK is surging in the polls, even overtaking Labour according to some polls. The AfD is now the second largest party in the German Parliament and they even broke out of their traditional heartland of East Germany. The far right won in Austria. The Swedish Democrats in Sweden are surging. David Leonhardt wrote that excellent piece about why left wing parties should be more sceptical of immigration and how the Danish Social Democrats maintained power by being really draconian on immigration.

So the main question, how should left wing parties deal with immigration? It's pretty clear that voters don't want Immigration, especially immigration from non white countries. Voters appear to be really hostile to social and demographic change and they very clearly appear to be prioritising this over economics. How should Democrats and the centre left deal with this? Should we just completely cave in to the far right, given that most voters seem to hate even moderate levels of immigration?