They do have constitutional rights, but immigration is not a right. SCOTUS has ruled before that that privilege can be taken away without due process. Just like any country has a right to reject immigrants for expressing support for terror groups, so too does the US. Now obviously this is a slippery slope, that I'm not particularly a fan of, but that is how the law works. There is a reason it's generally advised to not go to protests if you are an immigrant. More on reddit.com

If we're talking about Constitutional rights, such as those in the Bill of Rights, then yes, those apply to non-citizens. The Constitution protects persons, not just citizens. More on reddit.com

THE CONSTITUTION APPLIES TO ANYONE UNDER THE JURISDICTION OF THE USA REGARDLESS OF STATUS and this has been confirmed by the courts FAR TO MANY CASES TO LIST. People saying they don’t are either disinformation bots or uneducated in law. Here are some cases i threw together quickly: Rasul v. bush and Boumediene v. Bush guaranteed due process for prisoners of Guantanamo In U.S. v. Wong Kim Ark, an 1898 decision, the Supreme Court birthright citizenship is stretched to people born to illegal immigrants Plyer v. doe and Yik Wo v. Hopkins gave 14th equal protection clause Padilla V. Kentucky gave the right to legal counsel. Bridges v. Wixon (1945): The Supreme Court ruled that a noncitizen could not be deported solely for political speech, affirming that the First Amendment applies to immigrants. United States v. Alvarez-Machain (1992): Acknowledged that noncitizens in U.S. custody still have constitutional rights. There are far to many more to list that confirm more rights and back up the other ones listed More on reddit.com

Lets look at some text from the constitution. Article IV Section. 2. The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States. A Person charged in any State with Treason, Felony, or other Crime, who shall flee from Justice, and be found in another State, shall on Demand of the executive Authority of the State from which he fled, be delivered up, to be removed to the State having Jurisdiction of the Crime. It is pretty clear here what applies to citizens and what applies for any person. You can see the same thing, where citizenship is specifically called out, in other places but this bit has the example of both people and citizens built in. Now lets look at the fifth amendment No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation This is a limit on the power of government, not the granting of a right to a group. Since it limits the governments power there doesn't need to be a question of who is in the group or not, the government is simply limited in how it does business. The constitution is, in general, like this throughout. It says the government may do this or may not do that, but it doesn't split up the country into groups of people with disparate rights. The phrase 'the people' has been argued about, but current precedent holds that it is not limited to citizens. More on reddit.com