It is not even necessary for us to interpret the 14th amendment. The Senator from Ohio who wrote it, has already said what he meant.
That was posted here of FR some time ago. The purpose was to make the slaves citizens and to keep other out.
Luckily we rely on the text of the amendment, not on the comments of some legislator, in this case Sen. Howard (of Michigan, BTW), author of the Citizenship Clause. There was extensive debate at the time about the meaning of the amendment and Senator Turnbull and President Johnson, among others, weighed in on the side saying that it meant children of aliens would become citizens.
Like it or not the reality is we interpret amendments based upon what they say, and the Supreme Court is the venue we use to resolve disputes. So despite what Sen. Howard wanted the amendment to mean it actually means what the courts have consistently ruled for well over a century.