You misunderstand the sentence. A state must have some power before it passes a law, a power that gives it the right to pass the law. The states have the police power, and contract law is based on that power. It has nothing to do with religious belief, it has to do with the state constitutional power to pass laws.
No it isn't. Contract's are agreements between consenting parties. Criminal law is based on the police power of the state. Marriage exists independent of the power of the state and predates the power of the state. It is part of the English common law framework that was adopted wholesale by the original colonies and forms the foundation of the principles enshrined in the constitution. In fact, some were married outside of any state in the US? Are the not lawfully married?