This claim is False: They do indeed pay their taxes and if not are in some sort of deduction from their pay. No they cannot do jury duty because they are not legal U.S citizens.
The point of being a citizen is contributing to the general economy and common good of our nation while having a stake in both government and our justice and legal system.
https://www.americanimmigrationcouncil.org/research/adding-billions-tax-dollars-paid-undocumented-immigrants
This source above explains that: “the best evidence suggests that at least 50 percent of undocumented immigrant households currently file income tax returns using Individual Tax Identification Numbers (ITINs), and many who do not file income tax returns still have taxes deducted from their paychecks.” The end result is that undocumented immigrants are paying billions of dollars each year in taxes.
This defies Musk's claim.
What I think is important to keep in kind too is the power that Musk has. Many people could see this and take it and run, putting a target on the back of undocumented immigrants. Keep in mind, he posted this to which it gained a lot of attention on a media platform he literally owns.
While there is some truth in his statement regarding the jury duty, it seems a little harsh and redundant. Why would you want someone who is not a U.S citizen making decisions in a court that is not legally entitled to them anyway? He is making a point that jury duty is a chore for most citizens, but it still represents an important and integral part of our democracy does it not?
The American Immigration Council has a step by step breakdown on the tax information and also states that these undocumented citizens do not receive nearly the same benefits as an American citizen too. So he has a lot of parts of his claim that are strung out on misinformation.
There is a clear distinguishment of the rights and laws between citizens and non-citizens as the key is not residency, but citizenship.