Well. You’re the first person I’ve seen claim that the US constitution made a distinction between real citizens and those with Latin Rights!
A naturalized American citizen is a citizen in every way a natural-born citizen American is. The single distinction is that the naturalized citizen is not eligible to be elected President. This is quite different from the Latin Rights citizens of Italy, who had many disabilities, most notably no franchise.
The US Constitution is an operations manual for the federal government which operates under civil law inside the federal enclave and administrative law outside the federal enclave.
The States, with the exception of powers specifically ceded to the federal , or 'general' government, operate under civil, or common law.
In the states of Kentucky and Virginia, the privileges of alien friends depended upon the constitution of each state, the acts of their respective legislatures, and the common law; by these they were considered, according to the time of their residence, and their having complied with certain requisitions pointed out by these laws, either as denizens, or naturalized citizens. As denizens, they were placed in a kind of middle state between aliens and natural born citizens; by naturalization, they were put exactly in the same condition that they would have been, if they had been born within the state, except so far as was specially excepted by the laws of each state. The common law has affixed such distinct and appropriate ideas to the terms denization, and naturalization, that they can not be confounded together, or mistaken for each other in any legal transaction whatever.
This was the legal state of this subject in Virginia, when the federal constitution was adopted; it declares that congress shall have power to establish an uniform rule of naturalization; throughout the United States; but it also further declares, that the powers not delegated by the constitution to the U. States, nor prohibited by it to the states, are reserved to the states, respectively or to the people. The power of naturalization, and not that of denization, being delegated to congress, and the power of denization not being prohibited to the states by the constitution, that power ought not to be considered as given to congress, but, on the contrary, as being reserved to the states.
St. George Tucker, Blackstone's Commentaries