"You used to be able to just show up on a ship and they would make you a citizen if you were healthy."

Unless you were Chinese. Let's not romanticize that period, the Chinese Exclusion Act was enacted precisely over fears of too many people of a different culture and race moving into the US at once. It was only repealed in 1943, as Imperial Japan became the common enemy of both China and the US.

And the Jews who were seeking shelter from Nazi Germany weren't particularly welcome either. There was an entire conference in Evian in 1938, ironically organized by none other than FDR, that sought a solution to increasing Jewish emigration from Germany. The end result was that no one was willing to increase or waive any quotas.

History tends to repeat with some variations. Few political things are totally new under the sun.