Compositional error. Argument of the Stone.
The Federal government is bound by the 1st amendment. The States are not.
That said, most State constitutions carry similar wording and are bound by that wording. See your State constitution for details for your State.
You must also realize that your mind is your own. You are free to believe what you wish. No law, no imprisonment of any kind can change that. You are free to say what you will, though you are not free of the consequences of what you say. No law, no imprisonment can change that.
The 1st amendment does not gran any right. It only acknowledges the rights that are already there, and specifically prohibits the Federal government from interfering with it.
The States also recognize these rights to some degree. It is perfectly legal (if the State constitution allows for it) for a State to declare one religion or another the 'official' religion, just as they have done in the past. Nothing about that prohibits any religion, for it can't.
The "Appropriate law" is the 14th Amendment to the US Constitution, which forbids States from violating the rights that the Federal government is prohibited from violating.
Prior to the passage of the 14th, the protections in the Bill of Rights restricted only the actions of the Federal Government.
The US Constitution, for example, says that "Congress shall make no law respecting an establishment of religion..." This did not prevent the individual STATES from having an established religion, though (i.e. an "official State religion", and several of them did. After the passage of the 14th, though, that too became illegal.
The passages of the 14th Amendment, which bound the States to the Federal Bill of Rights, and the 17th Amendment, which called for the direct election of Senators, are the two biggest changes in the fundamental structure of the US since it was founded.
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While several States have such religious tests in their Constitutions, all such clauses are invalid. The 14th Amendment would make denying State elected office to an atheist a violation of his rights under the 1st Amendment to the US Constitution, and illegal. This question has been thoroughly litigated, and is settled law.
The governing case law is "Torcaso v. Watkins". Torcaso was denied a commission as a Notary in Maryland because Maryland had an oath requirement that required candidates for public office, and for certain types of commissions - including notries - to assert a belief in a "Supreme Being".
https://answers.yahoo.com/question/...HZ0aWQDBHNlYwNzYw--?qid=20081105172942AArLyFg