With all due respect taxcontrol, please consider the following.
What many people do not seem to understand about Congresss power to define the rules of naturalization is the following. Congresss power to define those rules is not plenary.
More specifically, the congressional record shows that John Bingham, Bingham the main author of Section 1 of the 14th Amendment which addresses citizenship, had indirectly indicated that not even Congress has the power to define natural born citizen with respect to both parents being citizens of the same country and owing allegiance to no other country.
”I find no fault with the introductory clause, which is simply declaratory of what is written in the Constitution, that every human being born within the jurisdiction of the United States of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen; but, sir, I may be allowed to say further, that I deny that the Congress of the United States ever had the power or color of power to say that any man born within the jurisdiction of the United States, and not owing a foreign allegiance, is not and shall not be a citizen of the United States.” - John A. Bingham, (R-Ohio) US Congressman, Architect of Section 1 of the 14th Amendment, March 9, 1866. Cong. Globe, 39th, 1st Sess., 1291 (1866), Sec. 1992 of U.S. Revised Statutes (1866), Cf. U.S. Const. XIVth Amend. (See top half of 2nd column)
That’s my tag line.
The 14th amendment was not passed until 1868. Until then, there was not a single restriction on Congress's ability to define citizenship any way it wanted to. Further, the 14th amendment with regards to citizenship, only limited congress's power by reinstating jus soli.
So other than the 14th amendment which specifically addresses citizenship, and the other more general provisos of the various amendments (equality clause, etc), the naturalization clause of Article I Section 8 is without restriction.