The missing piece to fill in the blank there is the 14th Amendment. The 14th Amendment gave clear definition to national citizenship and prohibited the states from restricting the basic rights of any citizen.
Here's how Section 1 of the 14th Amendment states the principle: "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. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws."