Try looking at it from another angle. Indians were not granted citizenship until 1924, LONG after the 14th Amendment. How (on what legal basis) did the 14th Amendment exclude Indians from citizenship?
Because the Native Americans were regarded as foreign powers and therefore not subject to the full jurisdiction of the United States.
Normally, there is a fairly clear distinction between what is foreign and what is not in a country: What is foreign is everything outside of the country. The Native Americans posed a unique challenge to this, as they were
within the United States, but were not regarded as part of the United States as everything else in it. They occupied a sort of middle ground between the United States and foreign countries like Mexico or Canada. Thus, the United States, while putting some regulations upon them, did not apply the full extent of its laws. While there has been a trend of increasing ownership by the United States of the reservations, they even to this day are not
fully subject to the laws of the United States. An obvious case of this is "Indian casinos", which have gained popularity because they can run a casino much more easily than anyone else due to being generally exempt from gambling laws.
This point was indeed made in the ratification debates, of how the Native Americans, at least the ones on their reservations, were unaffected by many laws of the United States. Senator Trumbull gave several examples of such, such as the inability to sue them in court ("Can you sue a Navajoe Indian in court?") or the fact the United States does not handle thefts or robberies they commit upon themselves ("Does the Government of the United States pretend to take jurisdiction of murders and robberies and other crimes committed by one Indian upon another?"). These quotes can be found in page 2893 of the 1866 Congressional Record, and were cited as examples of how they are not subject to the US's jurisdiction. While some of these examples ironically were negated because the United States
did take ownership of those (the Major Crimes Act caused the United States to take control of what it regarded as major crimes--murders, rapes, burglaries, larcenies, and arson--even when it is one Native American committing it upon another on the reservation), it still stands because it does not take control of
all crimes, as is the case everywhere else in the country.
Trumbull also further confirms that "If they are there and within the jurisdiction of Colorado and subject to the laws of Colorado, they ought to be citizens; and that is all that is proposed."
Heck, here's the full exchange. For some context, here they are arguing about whether the phrase "excluding Indians not taxed" to the Citizenship Clause should be done. Some felt this clarified that Native Americans were exempt, whereas others opposed it due to seeing it as unnecessary and opening up all kinds of questions about whether the government can just give citizenship just by taxing them:
Mr. TRUMBULL. Of course my opinion is not any better than that of any other member of the Senate; but it is very clear to me that there is nothing whatever in the suggestions of the Senator from Wisconsin. The provision is, that "all persons born in the United States, and subject to the jurisdiction thereof, are citizens." That means "subject to the complete jurisdiction thereof." Now, does the Senator from Wisconsin pretend to say that the Navajoe Indians are subject to the complete jurisdiction of the United States? What do we mean by "subject to the jurisdiction of the United States?" Not owing allegiance to anybody else. That is what it means. Can you sue a Navajoe Indian in court? Are they in any sense subject to the complete jurisdiction of the United States? By no means. We make treaties with them, and therefore they are not subject to our jurisdiction. If they were, we would not make treaties with them. If we want to control the Navajoes, or any other Indians of which the Senator from Wisconsin has spoken, how do we do it? Do we pass a law to control them? Are they subject to our jurisdiction in that sense? Is it not understood that if we want to make arrangements with the Indians to whom he refers we do it by means of a treaty? The Senator himself has brought before us a great many treaties this session in order to get control of those people.
If you introduce the words "not taxed," that is a very indefinite expression. What does "excluding Indians not taxed" mean? You will have just as much difficulty in regard to those Indians that you say are in Colorado, where there are more Indians than there are whites. Suppose they have property there, and it is taxed; then they are citizens.
Mr. WADE. And ought to be.
Mr. TRUMBULL. The Senator from Ohio says they ought to be. If they are there and within the jurisdiction of Colorado, and subject to the laws of Colorado, they ought to be citizens; and that is all that is proposed. It cannot be said of any Indian who owes allegiance, partial allegiance if you please, to some other Government that he is "subject to the jurisdiction of the United States." Would the Senator from Wisconsin think for a moment of bringing a bill into Congress to subject these wild Indians with whom we have no treaty to the laws and regulations of civilized life? Would he think of punishing them for instituting among themselves their own tribal regulations? Does the Government of the United States pretend to take jurisdiction of murders and robberies and other crimes committed by one Indian upon another? Are they subject to our jurisdiction in any just sense? They are not subject to our jurisdiction. We do not exercise jurisdiction over them. It is only those persons who come completely within our jurisdiction, who are subject to our laws, that we think of making citizens; and there can be no objection to the proposition that such persons should be citizens.
It seems to me, sir, that to introduce the words suggested by the Senator from Wisconsin would not make the proposition any clearer than it is, and that it by no means embraces, or by any fair construction — by any construction, I may say —could embrace the wild Indians of the plains or any with whom we have treaty relations, for the very fact that we have treaty relations with them shows that they are not subject to our jurisdiction. We cannot make a treaty with ourselves; it would be absurd. I think that the proposition is clear and safe as it is.
This is somewhat complicated by the fact that the US did later pass a law taking ownership of robberies and murders, but it still does not take jurisdiction of
all crimes as it does in every other part of the country. The point is clear: Native American reservations are not fully under the legal authority of the United States. This is why "Indian casinos" have gained popularity: They are exempt from gambling laws that everyone else is because of the limited jurisdiction of the United States (or states) upon the reservations.
In contrast, illegal immigrants
are subject to all the laws of the United States (the very requirement Trumbull gives). If one illegal immigrant commits a crime against another, they can be tried for it. They are fully liable to the laws of the United States.
As requested, this is the distinction between illegal immigrants and Native Americans.