The United States and Mexico are not at war. Clearly you are substituting emotional arguments for logical ones.
The point being debated is whether or not the mere physical presence of a person or persons within the territorial limits of a country fulfills the requirements of the Jurisdiction Clause of the 14th Amendment, especially when the physical presence is against the wishes of sovereign government of the country in question.
While the U.S. and Germany were at war in 1945, that does not change the issue to any significant extent. Let us change Patton's Third Army in 1945 to Pershing's Mexican Expedition of 1916-17 when the U.S. was not at war with the Republic of Mexico and Pershing's men were on Mexican soil whether the Republic of Mexico liked it or not.
Would the men of Pershing's Expeditionary force be considered "under the jurisdiction of the Republic of Mexico" as a result of physically being on Mexican soil?
No. Such persons not considered to be "under the jurisdiction of the Republic of Mexico".
Under international law, if you visit Israel with your family, can your 18 year old American citizen, non-Israeli citizen son be drafted into the IDF because he is physically on Israeli soil?
No. Your son is not considered to be "under the jurisdiction of the State of Israel" for such matters as he is a foreign citizen.
If the U.S. institutes a military draft, can the the U.S., under international law, draft a Mexican illegal alien and then imprison him for draft evasion if he refuses induction into the U.S. Armed Forces?
No. Under international law, the U.S. can deport him to Mexico or imprison him for illegal entry into the U.S. but it cannot imprison him for draft evasion because that Mexican national who is neither a U.S. citizen nor a U.S. resident alien (Green Card holder) is not considered, under international law, to be "under the jurisdiction of the United States" and it is therefore illegal, under international law, to draft him into the U.S. Armed Forces.
You can't have it both ways. If you have a class of people be they tourists, ambassadors, traveling merchants or merely illegal trespassers, you either have them "under the jurisdiction" of the country they are physically in or not.
"Jurisdiction thereof", in the originally intended context of the 14th Amendment, means the power, under international law, to send and legally enforce one of these:
If clauses are in the Constitution, they are there for a purpose and not merely to waste ink and paper.
If the "under the jurisdiction thereof" does not apply to a foreign trespasser who is illegally on U.S. soil and actively hiding from the U.S. Government, then who on Planet Earth does the "Jurisdiction Clause" apply to?
Who?