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I've now listed about 10 different major similarities, but if you'd like I can go on with more similarities.
Modern socialists in Europe are also starting to turn against immigration and toward ethnic nationalism as well.
This is a fundamental dark truth about socialism; it leads to anti-immigrant backlash. When the collective is paying for a lot of social welfare, they tend to get upset when people they perceive as 'other' come in and start to enjoy the fruits of the collective pie.
You can 1:1 map the increasingly closed immigration policy in the US with the rise of the social welfare state starting in the 1930s.