It is interesting,
Issodhos, that the very suit in question asserts
some of those Constitutional rights (as a basis for jurisdiction), but does not address (at least, I don't think so, without rereading it) the full panoply of Constitutional authority. I appreciate your reference and link to the GAO Report. I'll be reading that next. As to the distinction "between" rights, the U.S. Supreme Court has indeed had a long history of distinguishing between competing interests, and identifies some rights as "fundamental" and others - usually, but not always, unidentified by a Constitutional provision - as of a "lesser" quality. This has led to a three-tier analysis of government interference with such rights. "Fundamental" rights - and suspect classes - get a "strict scrutiny" analysis when addressing governmental infringements. (Footnote 6 of the GAO article discusses this concept briefly.) Lesser "rights" get a "rational basis" analysis, whereas some have received an "intermediate" analysis depending on the extent of the infringement and the strength of the government interest. Like you, I don't know that the Supreme Court should be in the position of opining on which rights are "fundamental" or not. The fact is, however, that they have.
Two quotes from the GAO report are relevant, whether or not they show a reasonable approach to the issue:
The Constitution does not apply in its entirety to territories solely by
virtue of the fact that those territories have come under the possession
and control of the United States.14 Whether rights under the Constitution
apply to a territory and, if so, to what extent depends essentially on either
of two factors, according to a series of Supreme Court decisions called the
Insular Cases.15 The first is whether the right in question is considered to
be “fundamental” or not; the second is whether the Congress has taken
legislative action to extend the Constitution to the territory.
and
The Congress can by law extend the coverage
of the Constitution in part or in its entirety to a territory or possession, and
has done so with respect to some territories. In the absence of such
congressional action, however, only fundamental rights apply. The Insular
Cases use the term “incorporated” to distinguish territories where all
constitutional rights apply, because a statute has made them applicable,
from “unincorporated” territories, where fundamental rights apply as a
matter of law, but other constitutional rights are not available.
