While the Constitution applies to all states, the question is does it apply to those areas NOT signataries to the Constitution. If the territories are signataries of the Constitution, they would be states when approved for membership by the Congress.
Congress however does not have power to make laws in territories. If the delegated powers are reviewed, one finds that Art 4 Sec 3 Pp 2 delegates the power to make needful rules and regulations for the territories but no mention of laws occurs. Logically, there was no need for this delegation if the other delegations concerning laws applied in the territories. How do federal laws apply/work in the US VI? Questionable!
The states have ratified the Constitution while territories have not, making the states a party to the Union. Are the peoples of the USVI citizens of the United States? Not under the 14th because the territories are not States and the United States are a Union of States, not territories. This is a complex issue which needs study regardless of what judges and other folks say. One needs to grasp what the legal term of art, The United States, means. The Constitution provides evidence the the term, United States, means the group of individual states (not a singular entity) as in the definition of treason: levying war against THEM or adhering to THEIR enemies (not "its"). Can Congress legitimately grant citizenship outside the delegations of power in the Constitution? Not legitimately (10th amendment).
Do the Rights enumerated in the Bill of Rights apply in the USVI? Yes because the BoR applies to all humans, everywhere. Does the constitution of the USVI recognize the BoR? haven't researched. Can Congress approve constitutions for various territories? Not under any delegation of power in the Constitution. Pls supply citation to correct me if possible. The Framers evaluated, offered and rejected allowing Congress to make new states from territories (Elliot's Debates, Meigs, The Growth of the Constitution.) At this point, Tom has raised an important question for the people's of territories.