Let's begin with the constitutional text, here from section 1 of the 14th Amendment:
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.
Once you have American citizenship, you have a constitutional entitlement to it. If you like your American citizenship, you can keep your American citizenship—and that's with the Supreme Court's guarantee, see Afroyim v. Rusk (1967):
