At least 12 members of the North Carolina House of Representatives (all Republican)--that's 10% of the NC House--want to go back to the good ol' days of the 17th century. Two members introduced, and 10 of them sponsored a bill to allow North Carolina to establish a state religion. The Rowan County Defense of Religion Act declares that, sure, the 1st amendment disallows any official religion or religious doctrine as part of federal law, but it says nothing about state law.
And yeah, okay, if you're doing a letter-of-the-law reading of the constitution, perhaps there's a case there. However, America has a common law system, in which ambiguities in the laws are figured out by the courts. North Carolina is a big 0 for 1 on court cases related to this matter: Forsyth County, NC lost a case in which they were sued for opening County Commissioner meetings with Christian prayers. Judge Trevor Sharp ruled that: the prayers that were used to open these meetings "referred to Jesus, Jesus Christ, Christ, or Savior with overwhelming frequency," and that such prayers "display a preference for Christianity over other religions by the government." The prayers, therefore, “alienates those whose beliefs differ from Christian beliefs and divides citizens along religious lines.”
The exact same issue came up again in Rowan County, NC, which was sued by the ACLU for opening their county commissioner meetings with Christian prayers. The bill addresses the Forsyth case by simply saying the NC General Assembly "does not recognize" previous court rulings on the matter.
Seeing as the bill already has the support of 10% of a heavily Republican House, it's certainly possible that this bill could pass, and from there it could conceivably make it into law. One has to think it would be dead on arrival in an inevitable court challenge.
As for the separation of church and state, America is forever torn by being a country founded on rational, secular principles while also being fervently religious. Rationality is winning the argument on gay marriage. Abortion is ongoing, but the religious side has more momentum. The issue is that religious values don't always apply to people who don't have them (gay marriage being the most obvious and current example), and so laws based on religious values rely on one's spirituality having objective validity. That's why North Carolina's futile charge here isn't just silly, it's morally backwards.