Presidents Washington, Adams, Jefferson, Madison, Monroe, John Quincy Adams, and Jackson were all born British subjects. None of them was a natural born citizen and they got grandfatered in under the exception in Article II Section 1. They turned out all right!
The first Naturalization Act passed by the first Congress in 1790 included the following exception: “the children of citizens of the United States that may be born beyond Sea, or out of the limits of the United States, shall be considered as natural born Citizens: provided, That the right of citizenship shall not descend to persons whose fathers have never been resident in the United States”.
Which was repealed when they realized their error.