Are you sure of that? Rights attributed generally to "the people" in the constitution can be limited from being enjoyed based on immigration.
For instance, "the people" have the right to keep and bear arms but god help you if you're here irregularly or on a tourist visa and do not meet one of the exemptions. Sure non-immigrants are persons but federal law doesn't give a fuck.
The second amendment is one of the few exceptions rather than the rule. It is difficult to argue for inclusion in "the people" who have the right to bear arms when excluded from selective service and from the definition of the unorganized militia.
Throwing in all these constraint when the constitution clearly say "the people" without qualification which magically means basically everyone one place but not most everyone somewhere else seems kind of arbitrary to me, but then again the courts seem to have held up visitors aren't people so hey. This is why I'm not a lawyer because really such fuckery makes my brain melt. If I were the sole sitting justice of the supreme court I'd say the qualification is a person is one unit of people and thus they have the rights of the people. IMO if you're one of "the people" then when the constitution uses "the people" unqualified elsewhere that's you -- which by symmetry means if you can't own a gun you're not a person and have none of the other rights of the people.
At least the 7th circuit agrees with you, (United States v. Meza-Rodriguez) even if there are other federal appeals circuits that don't. So this is something that will likely go to the Supreme Court eventually.