What did native-born Americans fear about immigration?

Nativists, as they were called, were profoundly hostile to immigration. They thought that immigrants constituted a threat to the way of life they valued and cherished. To them, immigrants were strange people speaking strange languages which they could not understand. They came from different cultures with radically different political and legal systems. Native-born Americans were afraid that the newcomers would radically change the very structure and nature of American civic institutions.
In the popular mind, immigrants were also linked to the twin dangers of anarchism and communism. Some of the more violent agitators of both movements were indeed immigrants. However, the vast majority of newcomers wanted nothing to do with any form of violent extremism. Nevertheless, during the Red Scare of 1919, immigrants, especially Jewish ones, were disproportionately targeted by the authorities, and many of them were subsequently deported using draconian laws.
Many immigrants were Roman Catholics, and native-born immigrants tended to belong to Protestant churches. Many of these people believed that Catholics owed their primary allegiance not to the United States, but to a foreign Pope in Rome. This was a long-standing prejudice among American Protestants, but one that gained added traction in the midst of mass immigration, particularly from southern Europe.
Nativism has been an aspect of American political life almost from the start. However, it only started to develop as a significant force around the end of the nineteenth century and the turn of the twentieth. The population of the United States had risen dramatically, leading to the growing expansion of cities, in which immigrants tended to congregate. Tensions rose as white, native-born Americans accused immigrants of undercutting their wages and driving them out of a job. The various strands of nativism came together in the rebirth of the racist Ku Klux Klan in 1915, encouraged by the hugely popular movie Birth Of A Nation, a film that essentially rewrote American history and shamelessly glorified the Klan.
In due course, nativism, and the pressures it unleashed, gave rise to the Immigration Act of 1924, which severely restricted immigration, especially from those parts of Europe with large Catholic and Jewish populations. It also stopped immigration completely from Asia and Africa. The Act was a blatant attempt to preserve so-called "100% Pure Americanism" and to maintain what the framers of the legislation deemed an appropriate racial and ethnic balance in the United States.
https://history.state.gov/milestones/1921-1936/immigration-act