The role of religion is to make one righteous and loving And politics means caring for people and their welfare. When religion and politics don't coexist then you have corrupt politicians and pseudo-religious leaders. A religious man who is righteous and loving will definitely care for the welfare of the whole population and hence becomes a true politician. And a true politician can only be righteous and loving. He cannot be anything but religious. All the Avatars and prophets have been caring for people and so were in politics. You can find many examples to this effect.
When religions restrict the freedom to worship and restrict modes of worship they become unsuitable for creating a harmonious society. When religion becomes all encompassing and gives full freedom to pray and worship in any manner -- that religion will bring righteousness and peace in people and will be suitable for any society.
People think politics and religion have to be kept separate because many religions did not give freedom to worship and did not care for all people equally. History has shown that religion has created conflict. But irreligious societies (e.g. communism) have created chaos and corruption.
Today both religion and politics need reform. Religion has to become broader and more spiritual to allow freedom of worship and broader to encompass all the wisdom in the world. And politicians have to become more righteous and spiritual.