“Subject to the jurisdiction thereof” has a very simple and obvious meaning, that the person does not have what we now call diplomatic immunity. IOW, if you break a law of the US, are you subject to punishment?
If yes, then you are “subject to the jurisdiction thereof.” If no, then you have diplomatic immunity and are not “subject to the jurisdiction thereof.”
In your first link, the author apparently does not understand that the several clauses of 14A address several issues that are not necessarily related. The 4th clause, with its prohibition of a future Congress repudiating the federal debt, has nothing to do with the 1st clause establishing who is a citizen.
The purpose of the 2nd and 4th clauses was to make it impossible for Congress to do some things that to our minds look so silly that there was no need to prohibit them: Compensate slaveowners for emancipation, assume the debts of the CSA or seceded states, or repudiate the federal debt, most of which was incurred during the War.
A problem is that of "Americans" who are really foreigners in their basic ideology. Many liberals want to eliminate any vow of fidelity in naturalization ceremonies, as they themselves seek to overthrow the Constitutional government, even if little by little.