Actually, one of those being denied entry to the U.S. is a native-born citizen. But in any event, the only distinction that our Constitution makes between the rights of native-born and naturalized citizens is that the latter may not serve as President of the United States.
But the oath taken by the naturalized citizen implies a contract. If it's later found that the oath was taken without "good faith", citizenship can be revoked and they can be sent packing. Most recently used with former Nazis who lied to get into the US.
"hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen; that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by law; that I will perform noncombatant service in the Armed Forces of the United States when required by the law; that I will perform work of national importance under civilian direction when required by the law; and that I take this obligation freely without any mental reservation or purpose of evasion; so help me God. In acknowledgement whereof I have hereunto affixed my signature."