(Note: This was originally posted as a reply to a friend's post on Facebook. I have modified it slightly to make sense without the original post.)
Do the rights listed in the Constitution apply to people who aren't citizens of the United States? I think it's clear intent of the text that they do. Let's look at something like 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."
The Constitution is using the term "person" here, not "citizen." I'm not a lawyer, not legal advice, blah, blah, but the implication pretty clear to me. The Fifth Amendment applies regardless of whether the person is a citizen or not.
It seems even more clear with the First Amendment. It's an injunction against Congress making laws. Congress can't establish a religion or prohibit the free exercise thereof. Granted, it says nothing about executive orders, but if it were Congress making a law preventing entry to the United States based on religion that would seem like to me a clear violation of the First Amendment.
The Fourteenth Amendment provides even more evidence, as Section One talks about both people and citizens separately:
"....No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws."
Since the first part specifically calls out citizens, the switch to person for the Due Process and Equal Protection clauses seems a clear indication to me, at least, that those cover non-citizens as well.
More importantly, though, we want these rights to apply whether a person is a citizen or not. Otherwise, there is too much incentive for those in power to remove their opposition by declaring them non-citizens and therefore no longer afforded the most basic protections of due process and against cruel and unusual punishment. Even if you trust the current administration, they will not be in power forever. Eventually someone you don't trust will be in there, and you'll want to ensure these protections remain.
Just my Saturday evening thoughts on Constitutional law here, though. Take them for the far less than two cents they are worth and nothng more.