There is no such thing as a person “naturalized at birth.”
That is complete gobbledygook.
Was there a judge in the delivery room waiting to lead the baby just emerging from the birth canal in the oath of citizenship and swear in the baby being born as a US citizenship?
It took my friend 10 years to be naturalized.
How can that happen ‘at birth?’
That is total nonsense.
If the person acquires citizenship at birth by virtue of some law that Congress has passed, that person has been naturalized at birth. Examples would be a person born outside the US to a US citizen, or a person born inside the US to non-citizen parents. These people are not natural born citizens, because by either geography or parentage, they do not have sole allegiance by birth to the USA. The constitution does provide congress with the authority to make law regarding naturalization.
If a person is a natural born citizen, (i.e. born in the country, and born to parents who are both citizens), then no law affects that person's citizenship either way. That person is a natural born citizen because they cannot be anything else.