So “who” has the right to due process: The US Constitution begins with the words “We the People of the United States”. The words “of the United States” becomes important to understanding those rights enshrined in the Fifth Amendment due process clause, which reads in part: “Nor shall any person….. be deprived of life, liberty, or property, without due process of law.” “Any person” clearly did not mean any person (anywhere in the world at any time) without caveat. We must go beyond “any person” to at least limit those within the United States, or citizens outside the United States (outside territorial waters, for example) who commit crimes and are prosecuted in the US.
We must also consider the preamble which defined “the people” as being “of the United States”. Native Americans who didn’t considered themselves part of the new nation wandered within and outside of the borders of the new nation stretching to the Mississippi. Similar groups from other nations contested US land, but were within our boundaries. Around a decade after the Constitution was ratified and during non-war hostilities with both Britain and France, Congress passed the Enemy Aliens Act. This allowed for the deportation of enemy aliens without due process.
No issue from the Court then. During the Civil War, Abraham Lincoln suspended Habeas Corpus and detained hundreds without due process. The Chief Justice of the Supreme Court held that Lincoln did not have the authority for suspending Habeas Corpus, but Lincoln disagreed.
The Constitution provides: “The Privileges of the Writ of Habeas Corpus shall not be suspended unless when in cases of rebellion or invasion the public safety may require it.” Lincoln believed he had the clear right and this was a national security issue for the executive.