If a politician can not represent different view points from their own they are a poor politician.To me this is more interesting from the standpoint of our representative government. Does an atheist politician represent his constituency if most of them are religious? Can a muslim politician represent a largely Christian populace? Or can one religious sect, that derides another (say southern baptist vs mormons, or something) represent that faction within their constituency?
Also, asking anyone to leave some core facet of their personality out of their decision-making is like asking a white guy to not be white, but only in these certain circumstances. A core belief will ALWAYS influence someone in their decisions, even if only subconsciously, be it religious or whatever.
To me one of the main functions of government is to protect minority groups. The majority and/or groups in power dont need help with their interests.
I firmly believe religion has no place in politics. One of the worst things that has happened in politics is the Christian right taking over the Republican party back in the 50s or so. Since then they have forced both parties to go away from true conservative/liberal view points and focus on moral issues that should not define being conservative/liberal. Those issues are not really something that should be in politics at all let alone the main issues.
Again if a politician can't put aside their religion and morals they don't belong in politics regardless of which side they are on. Governments role isn't to be moral police, particularly in cases where moral choices don't effect others.
A Muslim majority country should not force people to follow their beliefs neither should a Christian majority country.