Basically, a representative democracy cannot survive without religious, moral people running the show...
...but government cannot be the tool to force religion and morals onto the people. After all, everything the government tries to do gets screwed up, so why give it the chance to screw up our morales and religion?
The government continually enforces morality. It cannot make people moral, but it can punish immorality, for instance you cannot sell your body for sex, and you cannot inject illegal drugs into yourself. These are just a few of numerous moral enforcements. Most police departments have a Vice Squad that is specifically involved in enforcement of morality. How do you separate religion from morality? In my state you have laws against gambling, and you have many dry counties. I live in a city that is not allowed to sell alcohol on Sunday. These laws are rooted in the religious beliefs of the majority of voters that elect representatives to the legislature. Their religious beliefs inform their morality. Their morality determines how they vote.