If you had read Elk v. Wilkins, you would know it was not about the act you mention, and what I or anyone else thinks about the citizenship of Indians today is irrelevant. It was about whether an Omaha registrar of voters violated the Constitution by refusing to register Elk to vote in an 1880 election of local officials.
The specific question before the Court was whether Elk was, simply because he had been born within the U.S. and had voluntarily separated himself from his tribe and taken up residence among white citizens, "subject to the jurisdiction" of the United States within the meaning of the Citizenship Clause of the Fourteenth Amendment, and therefore eligible to vote as a citizen of the U.S. The Court held that he was not, because he had never been either naturalized or taxed and retained some vestige of allegiance to his tribe. It said Indian tribes were not, "strictly speaking, foreign states, but they were alien nations, distinct political communities . . . ."
The Court explained that:
The persons declared [by the Citizenship Clause] to be citizens are "all persons born or naturalized in the United States, and subject to the jurisdiction thereof." The evident meaning of these last words is not merely subject in some respect or degree to the jurisdiction of the United States, but completely subject to their political jurisdiction and owing them direct and immediate allegiance. . . .
Indians born within the territorial limits of the United States, members of and owing immediate allegiance to one of the Indiana tribes (an alien though dependent power), although in a geographical sense born in the United States, are no more "born in the United States and subject to the jurisdiction thereof," within the meaning of the first section of the Fourteenth Amendment, than the children of subjects of any foreign government born within the domain of that government, or the children born within the United States of ambassadors or other public ministers of foreign nations. (emphasis added)
I think the Elk Court's reasoning, as applied to children born within the U.S. to alien nationals, means that accident of birth alone does not make them completely subject to the jurisdiction of the U.S., and therefore does not make them citizens. The parents retain their allegiance to their own nation, and to some extent, so do their children. I hope to see Congress make a law expressing its will that this view of the Citizenship Clause should be followed, and the view the Court took in Wong Kim Ark, which is inconsistent with it, abandoned.