Jackson, very likely. Sotomayor, probably. Kagan, might fool us.
Very doubtful.
So that brings us to Kavanaugh and Barrett. Both are textualists - of course, as Kagan noted recently, "we're all textualists now" - and both tend to apply the ordinary meaning, or the plain meaning (the two are not coterminous, however, as "ordinary meaning" tends to refer more to the everyday usage of a term, whereas "plain meaning" will incorporate the more legal meaning of a term) of the language used. In this case, the phrase in question is "subject to the jurisdiction thereof" and the plain meaning of that term is that a person is subject to the jurisdiction of a sovereign if that person does not have immunity from prosecution under that sovereign's domestic law. Illegal aliens, whether domiciled in the U.S. or simply passing through, do not have immunity from prosecution under U.S. domestic law; accordingly, they are subject to the jurisdiction of the United States.
I give odds of 70% to 80% that Kavanaugh and Barrett take that approach, which gives another two.
Then there's Gorsuch, who is an interesting textualist inasmuch as he tends to be more of a literalist. A literalist plain meaning of the term also gets us to the same result, however.
I give odds of 60% to 70% that Gorsuch takes that approach, which gives another one.
That leaves Roberts, who, based on his ruling history, generally seems to take his role as Chief Justice way too seriously, inasmuch as he is often trying to maximize consensus on the Court.
Since I already have five or six, I give odds of 80% that Roberts holds with the majority in order to give as much oomph to the holding as possible.
That gives me a count of six or seven in favor of the straightforward plain meaning of the term.
The percentages favor the conclusion that the Court will hold that the term "subject to the jurisdiction thereof" means exactly what it says under the "plain meaning" (as opposed to "ordinary meaning") approach to interpretation.
No need to discover penumbrae and special secret meanings in the term.