These naturalization laws change all the time. I bet they changed a few times between 1790 and 1865. My father's family immigrated to Amercia after WWI, thought they became naturalized and got quite a shock when WWII broke out. Fortunately there were no internment camps for Brits in California. My uncle tried to enlist in the Army and Marines three times....then got drafted by mistake. Foreign enlistment rules for the military are something else that changes over time.
What was the legal status for Confederate veterans who immigrated during the War? Were they ever allowed to become U.S. citizens? I remember a thread about children born into the Confederacy. Evidently, no one challenged their citizenship after the War.