Human governments are established by God (Romans 13:1), but when human governments take it upon themselves to establish a religion of its own making, this is not good. It is the ultimate tyranny when governments of men step between the souls of men and God and establish a man-made religion its people are then forced to adhere to. Man-made, government-ordered religion is harmful to souls and is meant to chain men, and suppress real freedom and faith.
In the dark ages, government established religion was a nightmare. It was a way for men and women in politically high places to subjugate, enslave, and force its people to, in a round-about way, worship them, and not the only true God. An excellent example of government established religion today is the Taliban in Afghanistan.
In the biblical book of Daniel, in chapter 3, King Nebuchadnezzar of Babylon made a ninety foot tall image that he ordered all people under his authority to worship. Anyone who refused to worship his image would be killed. As we know, Shadrach, Meshach, and Abednego defied him and were saved triumphantly by God.
Revelation 13:11-18 tells of the latter day anti-Christ dictator (called the Beast) who will force the entire world, which is under his control, to worship the image most evil. This ultimate, ultimate tyrannical ruler will mix politics and his deceitful religion together to usurp the overall authority of Christ. He will force people to commit idolatry, or die; but, in the end, God will have His way (those who resist this last dictator have a special promise from God. Read Revelation 14:12-13).
Religion and politics do mix, in that persons in political power were put there by God, are accountable to God, and are ultimately deposed by God. God does not give these politicians the authority to establish religion and impose it on people. Faith is a free will-thing.