The children of the foreign-born go far beyond this. Immigrants hurt them the most, but they oppose immigration the least. How is this possible?
The best explanation is that the children of the foreign-born, like many other groups, are group-interested voters. They're concerned about the well-being of people they identify with, people "like them." The children of immigrants know what it's like to be an immigrant from first-hand experience. They know the misery of the Old Country, and the hardships of the New. And when they ponder immigration policy, their first thought isn't their wages. Their first thought is that the law is denying someone like their parents, cousins, or neighbors a chance to work for a better life.
Good point. It's interesting, though, that Cesar Chavez was at times strongly against both legal and illegal immigration. At other times, he was sympathetic to immigrants. Here's what Wikipedia says:
The UFW during Chávez's tenure was committed to restricting immigration. Chávez and Dolores Huerta, cofounder and president of the UFW, fought the Bracero Program that existed from 1942 to 1964. Their opposition stemmed from their belief that the program undermined US workers and exploited the migrant workers. Since the Bracero program ensured a constant supply of cheap immigrant labor for growers, immigrants could not protest any infringement of their rights, lest they be fired and replaced. Their efforts contributed to Congress ending the Bracero Program in 1964. In 1973, the UFW was one of the first labor unions to oppose proposed employer sanctions that would have prohibited hiring undocumented immigrants. Later during the 1980s, while Chávez was still working alongside Huerta, he was key in getting the amnesty provisions into the 1986 federal immigration act.
On a few occasions, concerns that undocumented migrant labor would undermine UFW strike campaigns led to a number of controversial events, which the UFW describes as anti-strikebreaking events, but which have also been interpreted as being anti-immigrant. In 1969, Chávez and members of the UFW marched through the Imperial and Coachella Valleys to the border of Mexico to protest growers' use of undocumented immigrants as strikebreakers. Joining him on the march were both Reverend Ralph Abernathy and US Senator Walter Mondale. In its early years, Chávez and the UFW went so far as to report undocumented immigrants who served as strikebreaking replacement workers, as well as those who refused to unionize, to the Immigration and Naturalization Service.
In 1973, the United Farm Workers set up a "wet line" along the United States-Mexico border to prevent Mexican immigrants from entering the United States illegally and potentially undermining the UFW's unionization efforts. During one such event in which Chávez was not involved, some UFW members, under the guidance of Chávez's cousin Manuel, physically attacked the strikebreakers, after attempts to peacefully persuade them not to cross the border failed.