So my question is how significant is the role of religion in the politics of the world today and how good is the effect on societies so far?
I don't know about the significance to me as a person because I couldn't care less about both (Politics and religion) but one thing I know is politics and religion are like inseparable twins. Religion is a mind control tool that can be used to lure masses into following a certain political leader/ruler or aspirant. Religion can build or destroy a political system. I think you have already seen such examples.