yeah why put in the clause “subject to the jurisdiction thereof” if they assumed everybody born here is automatically “subject to the jurisdiction thereof” of the USA anyway?.. they were clearly talking about persons born here with a lineage of parental ancestry that were from here not from a foreign land..
One way is that the phrase excludes diplomats, so subject to the jurisdiction is the distinction between possessing immunity and not.
The other way is that the phrase excludes those who have no allegiance to the US, such as sojourners and invaders; as well as those possessing diplomatic immunity.
Either way, the clause has an exclusionary function. The argument is the extent of the exclusion.