What were the ethical and civic issues with immigration in the 1860s to the late twentieth century?

This is obviously a huge question, but in many ways, the issues have not changed too much over time. The United States has long had a conflicted relationship with immigration, both welcoming the work and energy of newcomers and resenting them for threatening established social norms and taking jobs.
Before 1920, immigration was open to all except for Asians. Anyone could come. However, as more and more immigrants surged into the United States from Eastern and Southern Europe in the late nineteenth and early twentieth centuries, anxieties about them grew among native-born Americans of European descent.
Many of the new immigrants were Roman Catholic or Jewish and, from a civic point of view, were seen as not quite fitting into the dominant Anglo-Saxon, Protestant, Northern European culture. Many were not considered "white" or "Nordic" at that time. People already settled here were alarmed by the mix of languages and cultural practices and often considered the immigrants inferior. Being able to establish "colonial" ancestry became a mark of status in the US.
From 1920 to the 1960s, the US sharply curtailed immigration and established quotas to try to encourage immigration from Northern European countries while discouraging it elsewhere. This led to ethical issues, especially during the Nazi era. Because many of the Jews trying to escape the Holocaust came from countries with very low immigration quotas, many could not come to the United States and instead perished in concentration camps. The US did little to alleviate this situation, even while knowing the danger Jews were in.
In the 1960s, the US eliminated the quota system.