So the image above has been making the rounds on Facebook and appears to be showing a queue of immigrants, either in the late 19th or early 20th century, passing through Ellis Island or an equivalent port of entry into the United States. The tagline at the bottom says that these immigrants "never burned our flag, respected American culture, cared about America." With the top line it implicates that immigrants entering the United States in the 21st century, illegally, don't equal the same "higher quality" immigrants from a cultural protection perspective than these older immigrants.
First off, wow, the levels of cultural perspective shift held in that image, especially considering the widespread anti-immigrant feelings in the United States in the early 20th century specifically targeted at the above groups of immigrants is shocking. But I am going to let that go for now, because the reality behind this text line is also wrong.
This image if from 16 September 1920, and is from the bombing of Wall Street, an act of revolutionary violence which was, most likely, carried about by Anarchists attempting to disrupt the United States economy and political system. Although the United States government never formally determined who was responsible for the bombing attack, most evidence at the time and in later investigations points to a group of Italian immigrants, the Galleanists, a dedicated revolutionary group of Italian anarchists and followers of Luigi Galleani. This group was mostly made up of Italian immigrants and most certainly did not respect United States culture or care about America as it was in the 1920s, it was dedicated to the overthrow of the United States government and American society.
The above bombing by the way killed a total of thirty-eight people and was done with a massive explosive device planted in a horse-drawn carriage. It was detonated at noon to ensure maximum carnage. (The physical damage to the Wall Street building was left in place and can be seen today.)
The center point of this particular movement is pictured above, Luigi Galleani, an anarchist from Italy who was expelled from multiple European nations, and the Middle East, before arriving in the United States. He traveled the U.S. East Coast with a goal of motivating other anarchists, spreading revolutionary fervor among the working class, and supporting striking workers. He was a believer in "propaganda of the deed" - carrying out revolutionary violence to inspire others to join in. His followers are responsible for waves of assassination attempts (some successful), bombings, mass poisonings, and building a support network for anarchist activists through the early 20th century. (His newsletter was also a source of an early form of "doxing" - printing home addresses of leading capitalists to inspire his readers to direct action.)
This is just the tip of the iceberg when it came to immigrant activism, throughout that period Socialists, Communists, and other political dissidents came to the United States to spread their ideas and make a strong attempt at revolution within the United States. The Anarchists happen to stand out in United States history because they were more colorful than other efforts and far more aggressive in the use of violent tactics.
But broadly there is no magical period of dutiful, loyal immigrants who came to the United States that can be contrasted with the immigrants of today. Even in the late 19th through early 20th century immigrant boom in the United States you had efforts within that community to deliberately destroy the society and government of the United States, with any eye towards forging something new.
Sources: Wikipedia articles on the Wall Street bombing of 1920 and Luigi Galleani