0. Religious organizations - by those I mean organizations or individuals which hold great, almost all or all influence over a single religion right the Vatican Church, lead by the Pope, has over the Roman Catholicism.

1. Religious organizations relay on the dogmas of their religion being accepted to enforce it's will over large masses of people. It should be noted that dogmas usually are just beliefs they don't hold any notion of realism, trough it is not rare to be a influence of the real world situation in which the religion formed.

2. Religious organizations hold great power, even if not clearly seen, in the countries where they are greatly dominant. Power corrupts people.

3. Religious texts can be interpreted in many ways but religious organizations insist that their dogmas about such texts are the right ones. The fact that those higher in the religious organization can bend the dogmas to their liking is also common in religious organizations.

4. If you give religious organizations actual power or rule over the state it means that they hold even more power - leading to a faster and more widespread corruption.

5. If you are corrupted and have power you want both to keep and increase you power. So you remove all opposition and sent missions to bring your religion to pagans - or take their lands from their cold death arms if they refuse to do so.

END. Religious organizations are in the end mostly meant to give power to those which rule over them and for that sake are ready to do anything, even kill and erase from history. They impose a fixed social order, try to quell anything that would threaten their dogmas and generally are not positive, naturally there are exceptions to this to but they were and remain rare.
If they are given a influence (not to speak about practical rule) over a state it usually leads to even worse things as the possibility of their actions being stopped by the state to decrease. So nobody sane would want a union of state and a religious organization it usually leads to nothing good.