But what about birth tourism? What about people here illegally? Neither of those were a thing back in 1868.

But all of those people are subject to the jurisdiction of the United States. So they're all covered by the 14th Amendment. It's not legally relevant whether they have any other attribute. The 14th Amendment doesn't say that it doesn't apply to people who are here on tourist visas. Or who crossed the border illegally (or who crossed the border legally, but overstayed their visas). Or any other category of people, whether it was a thing in 1868 or not.

I'm not sure what you (or the folks pushing this theory) thinks the ambiguity is. This clause of the 14th Amendment only has one condition. It says affirmatively that it applies anyone born in the U.S. who is subject to the jurisdiction of the U.S. All of those people are subject to the jurisdiction of the U.S. So they'd all be covered.