FWIW, Woodrow Wilson’s mother moved to the U.S. at age 10. Her son wasn’t born until 20 years later. There’s a good chance she would have naturalized either through her father or on her own well before Woodrow Wilson was born.
That's a very good point. The naturalization act of 1795 would have naturalized her if her father became naturalized, so she might not have needed the 1854 law to make her a citizen.
I have always regarded the "Woodrow Wilson's mother was British" argument to be the logical equivalent of tipping over a flimsy chair in front of a pursuer while running away; A silly futile gesture of no serious consequence.