I think is quite implausible for a citizenry to be made up of a particular populace of church goers, and then completely ignore those ideals in their goals for the nation as well as their political requests. What we do ask of anyone in politics is that they abide by the Constitution and the Bill of Rights. If they want to promote a particular philosophical view or even religious view that doesn't violate these documents, then they are free to do so. However, the U.S. Supreme Court must always be vigilant in seeing that the propositions in these documents are not violated.
For example, if a fundamentalist Christian thinks that creationism is appropriate for schools, then they are free to pursue it in politics, but the courts must be wise enough to strike it down as religion if that is what they are teaching. On the other hand, this goes both ways. If a school system teaches metaphysical naturalism (no God) as a means to teach evolution, then the politicians are able to restrict such teaching if they so choose. An interesting question is whether the judicial system is within its rights to strike down such a naturalist position if politicians are not successful. I would say that they are not for the same reason that the judicial system is not in its rights to strike down an endorsement of God. Hence, I think legislators have a great deal of power in deciding which philosophical view local governments (or even at the national level) that will be endorsed.
Warm regards, Harv