"Once abolish the God, and the Government becomes the God. The fact is written all across human history; but it is written more plainly across that recent history of Russia; which was created by Lenin. There the Government is the God, and all the more the God, because it proclaims aloud in accents of thunder, like every other God worth worshipping, the one essential commandment: 'Thou shalt have no other gods before Me.'
"...Wherever the people do not believe in something beyond the world, they will worship the world. But, above all, they will worship the strongest thing in the world. And, by the very nature of the Bolshevist and many other modern systems, as well as by the practical working of almost any system, the State will be strongest thing in the world."
-- G. K. Chesterton, 1932
Removing religion from the public sphere, as per Chesterton, leaves a large hole for the State to fill. This is a decades-old warning that apparently has fallen on deaf ears, which is vexing, for those who fail to heed such a meaningful warning end up dooming themselves. Consider the totalitarian regimes of the previous century: inter alia, the Soviet Union, Red China, and even Nazi Germany (at least, when everything fell according to plan). In the case of the former two--both communist states--religion is held to be a counterrevolutionary, therefore subversive, force, a force antithetical to the State's grasp on power. And the Communist State will suffer no dissent. In the case of the last, it was all about the long game; when the Final Solution was delivered and the Jewish question "eliminated," the Nazis would slowly and surely subvert Christians, replacing faith in God with faith in the rule of the powerful, quoting Pope Emeritus Benedict XVI--the Sith Lord of Rome himself.
It is because we believe in something greater than ourselves that we can challenge our own creations and ultimately change the world. When belief is not an option, we end up worshipping the world in all its banality, but most of all, we end up gathering sacrifices to the Church of the State--some offering their very lives to it as human sacrifices. A world where the State is God would be more like Orwell's 1984. And Big Brother is the Almighty Father of this travesty.
The reason Church and State must be separated is because of the implications that would arise should the two be united: only a jackbooted, goose-stepping, totalitarian thug would seek to bind the two together in a union barely above the Twilight Saga (EXTRA HERESY! *BLAM!*) and thus consolidate power.
Those who truly value liberty know what to do. Tyranny demands Rebellion, after all.