How much did Chavez oppose illegal immigration? This article from 2014 in The American Spectator explains:

Call it the whitewash of Cesar Chavez. Yes, that Cesar Chavez: the late farm worker unionizer (he died in 1993) honored repeatedly by President Obama. The man the Left loves to name drop for his role in organizing all-those grape and lettuce and melon pickers in the day.

But there is a considerable twist to the story. In fact, Cesar Chavez believed ferociously in the border of the United States — because that border protected his union. So ferociously did he hold this view that the New York Times ran a story detailing an accusation that the union Chavez founded, the United Farm Workers, set up a 100 mile “wet line” to keep “wetbacks” and “illegals” — yes, all of those are Chavez’s words — out of the United States. So let’s go back in the time machine to the period when Chavez was rocketing to fame.

https://www.youtube.com/watch?v=lQ9jIXHhFJI

So. What’s the big deal, you ask? A hat tip here to Mark Levin, who brought up a startling fact: Cesar Chavez was deeply opposed to illegal immigration. But the question here is why.

The fact is that just as Americans along the southern border today want it sealed to protect their private property or the safety of their families, Cesar Chavez wanted desperately to protect his union from illegal border crossings by Mexican “strikebreakers.” At core, Chavez was demanding — like property owners along the border today — that the sovereignty of the United States be respected. Those who remember Chavez recall him vividly as a committed Chicano activist who neither minced words nor shied away from acting on his beliefs. And in doing so, he put himself firmly on record against illegal immigration…

On February 7, 1979, the New York Times ran a story in which the paper reported that Chavez, during a UFW-led seven-month-long strike outside Yuma, Arizona, five years earlier, had the union establish a “100-mile-long ‘wet line’ of military-style tents to halt the flow of illegal aliens across the border.” What happened? Said the Times of a strike led by Cesar’s cousin Manuel Chavez: “… hundreds of Mexican aliens were brutally beaten by UFW representatives to keep them from crossing the border and taking the jobs of striking melon workers.”…

Of course, it isn’t only the legal Mexican farm workers who suffered by the suppression of wages brought about by illegal workers, who are often paid cash under the table at a much lower rate than those they replaced. Here is a story by a white construction worker (a painter):

When I had my roof replaced several years ago, I contracted with a local company owned by an American man and his wife. When the crew showed up, however, many (if not all) were Spanish speaking. I don’t know their immigration status, but I can guess.