People are not subject to the jurisdiction of the United States when they are diplomatic personnel with diplomatic immunity. Invading military forces were another exception.
This provision has been interpreted to allow someone to voluntarily renounce their citizenship (i.e. you start out with citizenship if you are born in the United States or naturalized as a citizen, but can lose that citizenship if you voluntarily renounce it), but even someone who renounces their citizenship, and is located in the United States, is "subject to the jurisdiction of the United States."
This has been settled law controlled by binding U.S. Supreme Court precedent for 120 years.
Children of non-citizens have been considered entitled to birthright citizenship in the United States under the 14th Amendment since at least 1898:
United States v. Wong Kim Ark, 169 U.S. 649 (1898),1 is a United
States Supreme Court case in which the Court ruled 6–2 that a child
born in the United States, of parents of Chinese nationality who at
the time had a permanent domicile and residence in the United States
and were carrying on business there but not as employees of the
Chinese government, automatically became a U.S. citizen.
In this case the U.S. Supreme Court stated:
[T]he real object of the Fourteenth Amendment of the Constitution, in
qualifying the words, "All persons born in the United States" by the
addition "and subject to the jurisdiction thereof," would appear to
have been to exclude, by the fewest and fittest words (besides
children of members of the Indian tribes, standing in a peculiar
relation to the National Government, unknown to the common law), the
two classes of cases -- children born of alien enemies in hostile
occupation and children of diplomatic representatives of a foreign
State -- both of which, as has already been shown, by the law of
England and by our own law from the time of the first settlement of
the English colonies in America, had been recognized exceptions to the
fundamental rule of citizenship by birth within the country.
[T]he Fourteenth Amendment affirms the ancient and fundamental rule of
citizenship by birth within the territory, in the allegiance and under
the protection of the country, including all children here born of
resident aliens, with the exceptions or qualifications (as old as the
rule itself) of children of foreign sovereigns or their ministers, or
born on foreign public ships, or of enemies within and during a
hostile occupation of part of our territory, and with the single
additional exception of children of members of the Indian tribes owing
direct allegiance to their several tribes. The Amendment, in clear
words and in manifest intent, includes the children born, within the
territory of the United States, of all other persons, of whatever race
or color, domiciled within the United States.
The U.S. Supreme Court in this case also made clear that Congress does not have the power to override this Constitutional grant of birthright citizenship and this provision of the Constitution is "self-executing" and does not require implementing legislation to be effective:
The power of naturalization, vested in Congress by the Constitution,
is a power to confer citizenship, not a power to take it away. "A
naturalized citizen," said Chief Justice Marshall, becomes a member of
the society, possessing all the rights of a native citizen, and
standing, in the view of the Constitution, on the footing of a native.
The Constitution does not authorize Congress to enlarge or abridge
those rights. The simple power of the National Legislature is to
prescribe a uniform rule of naturalization, and the exercise of this
power exhausts it so far as respects the individual. The Constitution
then takes him up, and, among other rights, extends to him the
capacity of suing in the courts of the United States, precisely under
the same circumstances under which a native might sue.
Osborn v. United States Bank, 9 Wheat. 738, 827. Congress having no
power to abridge the rights conferred by the Constitution upon those
who have become naturalized citizens by virtue of acts of Congress, a
fortiori No act or omission of Congress, as to providing for the
naturalization of parents or children of a particular race, can affect
citizenship acquired as a birthright, by virtue of the Constitution
itself, without any aid of legislation. The Fourteenth Amendment,
while it leaves the power where it was before, in Congress, to
regulate naturalization, has conferred no authority upon Congress to
restrict the effect of birth, declared by the Constitution to
constitute a sufficient and complete right to citizenship.
It should be needless to say that an Executive Order may not alter a rule of law that the U.S. Supreme Court has clearly and consistently for 120 years held that Congress may not change.
Subsequent case law has made clear that domicile or permanent residence in the United States is not required for a child born in the United States to be a U.S. citizen.
For example, children of Canadian parents living in Canada whose mother had to be rushed to deliver their child in a U.S. hospital just across the border are dual U.S.-Canadian citizens, even though they were only on temporary visitor's visas for medical purposes.
Legal scholarship regarding the original intent of the language (even from conservative judges) supports this position:
Law professor Gerard Magliocca, the author of the definitive biography
of John Bingham, the Ohio congressman who was the principal draftsman
of the 14th Amendment, wrote a law review article years ago
To simplify, the words “subject to the jurisdiction thereof” weren’t
intended to exclude the children of ordinary foreigners living in the
U.S. Such foreigners are indeed subject to U.S. jurisdiction, meaning
that they are obligated to follow U.S. laws and can be punished for
failing to do so.
The words “subject to the jurisdiction thereof” were probably intended
to exclude the children of hostile noncitizens invading the U.S. (such
as some Native Americans) and the children of foreign diplomats, who
were entitled to some early form of diplomatic immunity.
Judge James Ho, a Trump nominee to the U.S. Court of Appeals for the
5th Circuit and an originalist himself, made a similar point in an
article before he became a judge.
The debate over the adoption of the 14th Amendment also reflects this meaning:
During the original debate over the 14th Amendment Senator Jacob M.
Howard of Michigan—the sponsor of the Citizenship Clause—described the
clause as having the same content, despite different wording, as the
earlier Civil Rights Act of 1866, namely, that it excludes American
Indians who maintain their tribal ties and "persons born in the United
States who are foreigners, aliens, who belong to the families of
ambassadors or foreign ministers." Others also agreed that the
children of ambassadors and foreign ministers were to be
excluded. However, concerning the children born in the United
States to parents who are not U.S. citizens (and not foreign
diplomats), three senators, including Senate Judiciary Committee
Chairman Lyman Trumbull, the author of the Civil Rights Act, as well
as President Andrew Johnson, asserted that both the Civil Rights Act
and the 14th Amendment would confer citizenship on them at birth, and
no senator offered a contrary opinion.
Footnote On Indians Not Taxed
The "Indians Not Taxed" clause of the 14th Amendment, by the way, became moot in 1924 when all Indians in the United States were made subject to U.S. income taxes by statute in the Indian Citizenship Act of 1924. Specifically:
The Indian Citizenship Act of 1924 provided "That all noncitizen
Indians born within the territorial limits of the United States be,
and they are hereby, declared to be citizens of the United States".
This same provision (slightly reworded) is contained in present-day
law as section 301(b) of the Immigration and Nationality Act of 1965
(8 USC 1401(b)).