Young royal children of today aren’t formally addressed by titles anyways so I don’t understand the fuss. Moreover the children will probably live and stay in a country where titles aren’t recognized.
Just want to clear up a fine point here: The United States doesn't grant its citizens titles, but it does recognize foreign titles. For instance, when President Biden ordered the flags to half-staff last week, he did it in honor of Queen Elizabeth II, not Elizabeth Windsor.
Even informally, if people have titles, they can use them here. Just recently I was filling out a form for an art museum membership that included a check box for "Prince/ss" as a title, along with Mr., Mrs., Ms., Dr., etc. It's rare, but not unheard of.
The U.S. Constitution prevents states and the federal government from bestowing titles, and it blocks office-holders from accepting them (or other gifts) from foreign princes. But, non-office-holders (like Grace Kelly or Meghan Markle) can hold titles.
There's also an immigration rule that requires people seeking U.S. citizenship to renounce their foreign titles.
So, to recap:
Lilibet: Born in the U.S. to an American mother, she has automatic U.S. citizenship. She keep (and use) her titles.
Archie: He is eligible for U.S. citizenship since he has an American mother who resided in the U.S. for five years before he was born, but he probably wouldn't have received U.S. citizenship automatically since he was born in the UK. He can use his titles now, but if he decides to seek American citizenship in the future, he might have to give them up.
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