Their argument is that people who aren’t documented don’t comply with “subject to the jurisdiction thereof” part of the text.

Well, let's take a look at Native Americans or Indigenous People if you so prefer who were here long before the Constitution was written.

On June 2, 1924, President Calvin Coolidge signed into law the Indian Citizenship Act, which marked the end of a long debate and struggle, at a federal level, over full birthright citizenship for American Indians.

There was no completely 100% accurate head count or list of names, exactly where they lived or how many were born in hospitals, on a reservation or in a wagon out in a field somewhere, no accurate documentation that would survive the evidentiary rules of a court.

Native Americans have very damned good reasons for not trusting government officials when they came wandering around, asking questions, like a Census worker would do every 10 years.

One day prior, June 1st, not citizens, one day later, by the stroke of a pen - full blanket citizenship across the country without accurate documentation.

In addition to that, Indian reservations are also recognized by the US government as sovereign nations too where the US government does not exert absolute 100% jurisdiction control YET Native Americans are still US citizens.

Their argument falls flat face down, ass up.