[epistemic status: Quite uncertain. I’ve spent a few hours reading about this over the last few days, but I’m not very knowledgeable about anything here. If I’m wrong, it’s probably because there’s historical context which makes Chavez’s actions more reasonable. I tried to look for this kind of context a little, but couldn’t find it quickly so stopped looking.]
Cesar Chavez, as far as I can tell, overall made the world a worse place by doing immoral things. I don’t see why he should be memorialized.
I’m mostly upset by all the shitty things he did while opposing Mexican immigration. One columnist wrote at the time: “Cesar Chavez, a labor leader intent on protecting union membership, was as effective a surrogate for the INS as ever existed. Indeed, Chavez and the United Farm Workers Union [UFW] he headed routinely reported, to the INS, for deportation, suspected illegal immigrants who served as strikebreakers or refused to unionize.” (from , but see also )
His UFW patrolled the US-Mexico border, trying to stop Mexicans from crossing. They were like the Militiamen, but more violent: directed by his brother Manuel, on at least a few occasions they beat Mexicans who were trying to cross the border.  
And he deserves a lot of the blame for the immigration restrictions which meant these Mexicans couldn’t enter the US legally. He first rose to prominence opposing the Braceros program, which was a guest worker program allowing Mexicans to work as farm workers in the US with a variety of pretty reasonable-seeming conditions—all their contracts had to be in Spanish, their employers had to provide free medical care, and so on. This program reduced the bargaining power of workers who already lived in the US. So Chavez organized strikes and protests; this seems to be a major factor leading to the program being cancelled. (The program seemed to be quite bad in several ways, but overall I think it was still much better than not letting those people work in the US at all. Read more about this here:  )
He also did a bunch of things which all seem somewhat petty and power-hungry: the UFW ended up in violent conflict with the International Brotherhood of Teamsters because the IBT was representing farm workers, and his union thought that it should get to represent all the farm workers. A few of the people from UFW got killed. I don’t understand what happened here well enough to decide whether I think he did the wrong thing or not, but I’m skeptical. His insistence on not allowing semi-autonomous local chapters of his union similarly seems kind of sketchy to me.
One thing that surprised me about this story is how willing Chavez seemed to be to hurt Mexican farm laborors for the sake of his union of Mexican farm laborors. The cynical reading is that he was power hungry, but the more idealistic reading of his whole life is that he really believed that unions were the way forward for the world, and he was so single-mindedly focused on achieving this that he didn’t notice how many millions of lives he made worse by his actions. I think the idealistic option is even more depressing.
I feel kind of dumb complaining about a Chavez state holiday while Columbus Day is still a thing. But the truth is important. As  writes:
I raise this issue because it speaks to a gaping hole in this nation’s historical memory. The fact that craven politicians-of every stripe-will lie with impunity in order to advance their agendas is nothing new. However, the notion that they can so easily manipulate the public in an age where access to information is quite literally at the fingertips of each and every American, should be profoundly disturbing to anyone who values our republican form of government.
If the philosophy of such an historic figure-who was alive less than two decades ago-can be willfully distorted-despite the abundance of evidence clearly establishing his views on this subject-in pursuit of a tendentious agenda, then what hope is there for engaging in an honest, open debate during this most contentious of presidential elections? [Note: The author wrote this in 2012, talk about “most contentious of presidential elections”.] If the American public is not able to differentiate fact from fiction, then what hope is there that it will make an informed decision as our country casts its ballots this November? As the great Spanish philosopher, poet, and novelist George Santayana once wrote, those who cannot remember the past, are condemned to repeat it.