I would argue that this is indeed impossible. Ed Milliband and Nick Clegg are Atheists, this is going to affect their decisions whether they are conscious of it or not. Tony Blair was openly Christian, as is George Bush. Did this affect their decision to go to war? Was the claim of bringing stability to the middle east a smokescreen for a holy crusade against the infidels?
Every issue I take on is guided by my beliefs about morality, reality and the truths about the universe, and it was these beliefs that guided me to my chosen political affiliation. Hence the blank stares when I argue that, despite Ashford needing more houses (a view I'm not convinced of anyway) the land doesn't want to be built on, the trees don't want to be chopped down, they should be left alone for their own sake.
My belief is that all things have inherent value, and cannot and should not be judged only on their usefulness to humankind.
The point is that this is my belief and will guide my every move, word and thought so, as a representative of Ashford Green Party and 1014 voters I have a duty to be open about where my decisions and actions come from.
To 'take religion out of politics' would only cause politicians to hide what they believe, with a danger that Atheists would take over, effectively creating a theocracy that those of us with different beliefs will not be able to challenge. No faith should have total control, all should be considered and our representatives have a duty to be open about their beliefs, so we at least know where their moral compass is pointing.