re: North Carolina and State Religion (Constitutional re-cap)
When written, the US Constitution did not prevent North Carolina from establishing a state religion, outlawing newspapers, etc..
After the Civil War the Constitution was Amended, with the 14th Amendment guaranteeing some baseline of rights for all persons within the United States.
Then, over a long (still going on today) series of federal judicial decisions that we call "incorporation" or "the incorporation of the 14th Amendment," certain rights were expanded (and State power reduced)
When we talk about rights in America we are talking about limitations on government. "Congress shall make no law..." and such.
The Federal rights given meaning in the form of limitations on the federal government came to also be limitations on State governments.
What conservative wackos mean when they say North Carolina can have a state religion is that they reject a century of interpretation of the 14th Amendment as being broadly limiting of states. If one holds to a theory of the Constitution wherein North Carolina can have a State religion then NC can also probably ban newspapers that criticize the state government and limit the free exercise of minority religions.