The law woulod have been the Naturalization Law of 1802.
Statutes at Large, 7th Congress, 1st Session
My grandparents were born in 1893, 1894, and 1895 (x2).
They were never naturalized.
You need to step back one more time.
Were the parents of your grandparents naturalized?
2 of the 4 were eventually, but not at the time their children were born.
My point was, all four of them lived their entire lives as US citizens and were so recognized by the US Navy, the US Army, the Board of Education of the City of New York, and the Board of Elections of New York State.
The only mechanism by which they acquired their citizenship was that they were born here.
Now, it is true, when THEIR parents stepped onto the ships that brought them here, they never intended to return to Ireland or Germany and they intended for their children (if any) to be Americans.
It's also true that when I studied the US Constitution in 1966 (thank you Mr. Benofsky) I was taught that being born here conferred citizenship.
I concede that in 1895, or 1966, the number of people here illegally was tiny (there were ads on the TV in NY right after Christmas every year when I was a kid reminding aliens to register by January 1, and asking citizens to turn in ones who didn't).
I think there is a case to be made that the children of illegals as presently defined do NOT acquire citizenship at birth - I just think it's a case that no US court will ever recognize, so an Amendment will be needed to solve the problem.
A statute covering naturalization has no bearing on someone that is already a citizen by fact of birth.