I'm not arguing based on the law. I am an original intent constitutionalist. The 1790 law is the strongest evidence of original intent. Yes, the natural born citizen portion was stricken. But it wasn't replaced. In fact, the phrase "natural born citizen" has never again been written into U.S. law.
Are you a Cruz supporter, because you sound like many of the Cruz supporters that I constantly argue with who twist law and logic to say Ted is eligible. The 'Natural Born Citizen' clause was stricken and yes,
REPLACED, in the 1795 Naturalization Act. As you can see, from the pictures I provided, that 'NBC' was replaced with 'citizen' and this legislation became apart of and known as "an act to establish an uniform rule of Naturalization". If Congress changed the law to only consider these children born abroad "citizens" and no longer "natural born citizens", then why weren't similar changes made to ARTICLE II, SECTION 1, CLAUSE 5 of the US Constituion? If the Founders or Congress at the time had intended for these children born abroad to be Natural Born US Citizens, then why was that phrase alone eliminated entirely in the 1795 Naturalization Act?
1790 legislation has no legal bearing, as you've admitted I think, and carries no more of an "original intent" than the 1795 legislation. The 1790 legislation was repealed only 5 years later, under the Presidency of George Washington, while many of the Founders were still alive. How many more Founders became President after the 1795 Naturalization Act, and yet still none of them or anyone in the Legislature reverted back to this 1790 definition for children born abroad? The 1790 legislation does not represent the original intent of the Founders, it more likely represents an error of Congress at the time; one that was fixed just 5 years later. Where the Constituion gives Congress the authority to establish naturalization codes for admitting foreigners into US citizenship, this and Ted Cruz's claim to citizenship fall under that provision.
The phrase "NBC" was never written into law again because it is common sense and to be understood as such that a "NBC" is one who is born on US soil. There was never any need to establish standards for "Natural Born Citizens" or to mention it in legislation.
Even in the very eligibility clause itself (ARTICLE II, SECTION 1, CLAUSE 5) the Founders used both the terms "Natural Born Citizen" and "Citizen", so the Founders and the Congress at the time knew there was a difference between the two terms and made the point to differentiate between the two.