Politics and Religion

Can we really separate religion from politics?
Is it possible? Because from what I have seen and experienced.
Religion has politics. Religion IS politics.
The only difference is Religion is utilizing God/Buddha/Allah/etc. as a tool to get others to believe that what their saying is true and that makes them follow their teachings.
Also, Religion has a Hierarchy. For the Catholics, we have the pope. The methodist has its Clergy. The Buddhist has its Monk. and so does other religions. They have their own president for each and every religion that we have now.
Yet, they say that the politicians should not interfere with the church decision but the churches can intervene with the voters' thoughts, their feelings, their actions.
So, can we really separate Religion and politics?