At first I wanted to say that they're morons. And they're still morons, but it seems they're aiming to limit what the Federal Government can do to the state:
(Here's the Bill in question)"Whereas, the Establishment Clause of the First Amendment of the Constitution of the United States reads:"…Congress shall make no law respecting an Establishment of Religion, or prohibiting the free exercise thereof;…"; and
Whereas, this prohibition does not apply to states, municipalities, or schools; and
Whereas, in recent times, the federal judiciary has incorporated states, municipalities, and schools into the Establishment Clause prohibitions on Congress; and
Whereas, the Tenth Amendment to the Constitution of the United States reads: "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."; and
Whereas, the Tenth Amendment of the Constitution of the United States prohibits the federal government and prohibits the federal courts from expanding the powers of the federal government beyond those powers which are explicitly enumerated; and..."
...Mmmmkay. Let's skip ahead to the end before getting to the middle:
"SECTION 1. The North Carolina General Assembly asserts that the Constitution of the United States of America does not prohibit states or their subsidiaries from making laws respecting an establishment of religion.
SECTION 2. The North Carolina General Assembly does not recognize federal court rulings which prohibit and otherwise regulate the State of North Carolina, its public schools, or any political subdivisions of the State from making laws respecting an establishment of religion."
Unless I bear grievous misunderstanding of things, the Bill of Rights should be considered to be the unquestionable national law. It applies to all states and the Federal Government alike. Under this guise, I would assert that, whereas it may be unconstitutional for the Federal Government to dabble in anything religious, it is likewise (or ought to be) unconstitutional for State Governments to do the same. Thus... the bill is fundamentally flawed. What I presume to be the intent of the bill, however, is to counteract any of the actions which the Federal Government may be taking in the Public School System that the State Legislature deems to be abridging the 1st Amendment. ...Which they intend to do by doing something equally unconstitutional.
In short, this seems to be a means of deregulating Federal mandates with respect to the practice of religion in the State's Public School System.
Now, to an excerpt from the middle, starting at line #15:
"Whereas, the Constitution of the United States does not grant the federal government and does not grant the federal courts the power to determine what is or is not constitutional; therefore, by virtue of the Tenth Amendment to the Constitution of the United States, the power to determine constitutionality and the proper interpretation and proper application of the Constitution is reserved to the states and to the people; and
Whereas, each state in the union is sovereign and may independently determine how that state may make laws respecting an establishment of religion; and..."
Someone forgot about the Supreme Court, and what makes the Supreme Court so good (at least in theory), the 11th Amendment! The intent of the bill may be to give back some values to Employees of the State/Federal Government (this will be addressed shortly) within NC, but the rhetoric is just vile. By this logic, it means that a state has the right to interpret the Bill of Rights, and perhaps any other Amendment. That's... not right, not at all. Likewise... I'm not sure it's fully right for the Federal Government to the same - let me explain that one: Regarding the Bill of Rights, the writing is kept (despite its age) quite clear and easily understood to those that are actually literate... the latter might be becoming an issue, though that's out of scope here. The point one should strive to make in this is that, unless an amendment is repealed (and there is a specific process for that), neither States nor the Feds have the right to pass legislation which violates your rights. Unfortunately, they both do that a lot.
Now, the last bit:
"Whereas, Rowan County, North Carolina, asserts that the protections afforded to citizens of the United States under the First Amendment are not in any way to be abridged when such citizens become government actors by virtue of their appointment, election, contract, employment, or otherwise engagement; and
Whereas, Rowan County, North Carolina, requests and encourages the North Carolina General Assembly to pass a resolution declaring that the State of North Carolina does not recognize the authority of federal judicial opinions arising from the exertion of powers not granted to the federal government by the Constitution of the United States; Now, therefore,
Be it resolved by the House of Representatives, the Senate concurring:"
...See the second block of quotes, or line 31, for the verdict. But you already read that.

So, again. I have to guess that this bill is born from teachers as government employees having the right to express themselves being reduced due to... being government employees. If you know a teacher in the public school system, you may have heard them talk about what they can't talk about (belief-wise) in class due to school policy, and that is a violation of their rights that should not be waived.
...However, the means by which the bill aims to address the issue is completely flawed. And even unconstitutional.