The idea that each citizen gets to vote means that politicians who ignore the opinions of their voters will not do well.
With that said, a moral politician will have to decide when they think the voters ideas are too stupid to indulge.
I suspect the question was asked in a more philosophical manner, but politics is about what is possible, more than what is perfect.
I'm Australian, so I'm basing this off what we do here.
The national policy here in Australia promotes the separation of church and state, that is that religion and religious institutions should have no weight on the political field (why then churches are not taxed is a debate for another time).
In response to gordonjames, I absolutely understand what you're saying. The thing is, that it can just as easily be a moral belief that you may hold, without necessarily having to tie it on to a religion. If your moral ideologies fit together with your religious doctrine, then great. But religion alone should not be a cause for political force. Do you get what I'm saying?
The Constitution clearly call for a separation of "church/religion" from the "state." Politics refers to governance — organized control over a human community, particularly a state. There for in matters of public policy to particular religion holds sway. Of course one's religion is likely to affect one's opinion, as in the access to therapeutic abortion debate, but as a matter of public policy pragmatism is necessary.
When you look at religion in politics you have to realize that it truly has no place. However, one needs to only look at history to understand that religion has shaped politics for thousands of years and it will most likely continue that way. The United States used to be a pluralist Christian nation where the Constitution and many other laws were centered around the Christian religion. Evidence of this can be seen all throughout the United States, such as with judges holding oaths over the Bible and mentioning of "God" in the pledge and on the currency.
Now, religion should be becoming less of a valid argument in any debate. As the world progresses to a secular society, the oddities such as the moralist Islamic states and the Atheist China, clearly need to be dealt with in order to achieve a form of unity. Religion in those moralist or atheist states play a HUGE role in their politics, but they don't necessarily belong there.
Judges and political figures in the United States used to use religion a lot back during the Cold War. Society was built upon religion where homosexuality and communism were considered to be some of the greatest sins of mankind. McCarthy became popular because he used religion to force out the communist atheists and it was during this time when we added "Under God" to the pledge. Ronald Reagan also used religion to his advantage, but it was under the same purpose as before, "prove that Christianity is better than communism".
Now that the ideological wars are over, religion seems out of place when being used as an argument. Politicians don't go around quoting the Bible in debates as people are becoming less and less interested in religion. Religiosity is declining in the United States as the "Great Awakenings" are at an end. Using religion now to gain support will not "rally the crowds" as people want more dependable politicians. Still, some people do use religion in debates, though hopefully religion will be fully separated from the state like it should be.
Supposedly every voter gets a say in how their elected official operates. But there's a multitude of problems that arise if a particular group were to gain leverage on the (supposedly) un-religious and unbiased government. It was a step back when it happened in the 50's to combat communism, and it'd be a step back if we did it again.
So no, religion is completely invalid when it comes to making real life decisions for our country.