This subject is a tricky one, as religion and faith are inexorably intertwined. To this end, I'll begin by distinguishing religion & faith conceptually, then will explain the deeper links between religion & the state, ideally in an attempt to prove they are in essence the same concept.
What is Faith
I personally have faith in something that I find undefinable. Every time I try to define it, it comes out a rambling nonsense. If you must label it anything, generic Christian is close, though there is much about that particular organised religion that I wholeheartedly disapprove of. That faith, however, gives me no right to make others live my way. That is fine by me, so long as I can live the way I want to myself. This is the primary distinction between faith and religions, however - one is personal, the other is public.
Where Faith Ends & Religion Begins
A person's faith ends with themselves. It's a personalised view of the beliefs you have, and how they impact you as an individual. A religion, however, is a collective & organised definition of faith.
They tend to have hierarchies, rituals, tithes, and laws based on some traditional definition of morality for society, while faith simply dictates an individuals morality. Religion, being a shared belief set, affects all who share in the belief at minimum. If that religion is also enshrined as law, it can impact anyone in a region, regardless of what the individuals of that region believe.
Religion & Divine Right
Religions have always claimed that their deity has the divine right to rule the people. The priests, as intermediaries between the mortal and the divine, originally held this right by proxy. In the end, however, the God was the only one whom ever had such power, and such powers returned to the God once a priest died.
Religion & States - A Brief History
Since the dawn of civilisation began, society has had religions. We have as a species sought the "why" to all the great questions, and when the answers are unknown we historically made up a reason ourselves. In the early days of civilisation, we had no science to provide logical answers, so we used faith & gods as a means to answer such questions.
Early on, the power of governance resided in the priesthood. To consolidate this power, the priests gave temporary power to nobles. To begin with, kingship was bestowed by priests on nobles (usually by marrying off the high priestess to a candidate), with the king being allowed to rule in times of plenty, & sacrificed in times of hardship. This dynamic changed once dynasties began to form. After a few thousand years, we eventually had nobles claiming the divine right of kingship without the priesthood's prior involvement (Sargon III of Akkad).
Kingship, Government, & Divine Rule
The idea that Kingship was bestowed on individuals via their blood has existed since then until today, as monarchs still exist. However, all kings have always claimed their power to rule others comes from a God. So long as they follow God's law, they can make just and benevolent decisions for others because they have that divine right to rule. This conditional following of faith is the main reason why King Henry VIII created the Church of England - with that, he could break accepted Catholic beliefs on marriage, without invalidating his divine right to rule.
This premise survived as a concept for thousands of years, and only began to lose traction to other forms of government with the French & American Revolutions. It was at this point that the revival of the ideas of democracy and Republics returned to the fray.
Divine Right & Modern States
Even though kings were dismissed by the ideas of republicanism and democracy, the concept of the states, governments, and the existence of "divine rights" survived. Instead of being inside a person, however, those rights were instilled into the system of government & the newly formed constitution. So, in a modern society, the government has assumed the power of God, but gloss over this fact by claiming their mandate comes from people.
However, there is a problem with the idea that the people have the divine right to rule. No one since the days slavery was socially acceptable has considered it okay for an individual to force anyone to act without consent. So if no one person can tell another what to do, why is it a group can get that power.
Let's turn this into a maths equation.
Let x represent the number of people who are in society.
Let y = the % of people with the divine right to rule another without consent.
We can stop there to be honest, because no one in a Republic or a democracy can claim to have divine rights. Thus, y will always equal 0 in the above equation. Ergo, no matter how large the society (x), the strength of society's right to use forceful rule over another will always equal 0.
Religion & the State - Food for Thought
Since society cannot claim the right to rule others, but the state can, then logically, the state must be considered a divine being in an of itself. It cannot claim that God gave those rights to the state, nor did the people. Some men, long dead, signed an agreement once, voluntarily. No one alive has joined them in that agreement, and those men never claimed God bestowed them or their positions with divine powers. Ergo, those who believe the government works for them and can help us have given up their faith to their new God, the state.
This presents a serious problem to worshippers of any form of Judaeo-Christian God. "Thou shalt not worship any other God" is RULE # 1 in both faiths. But all statists believe the state has God's rights, without any link to God or individual consent. The follower of any derivatives of either Judaism or Christianity is a hypocrite if they believe the state has the right to rule others without consent. They also are damned by their own rules.
The New World Religion
People can deny the state is their new God, but it's the only logical conclusion one can draw. Once you start looking at it that way, many parliamentary systems, and the US government itself, really start looking like the popular organised religions.
The government buildings are the churches. The politicians are the clergy. The civil servants are the acolytes. The diehard left and right are the zealots. The vote & petitions are prayers. The taxes are tithes. The law is the Holy writ. The sessions of Congress & Senate are the ceremonies. They have costumes, altars, and holy idols in the form of robes & suits, podiums, and flags (which these days people treat with as much deference as the cross).
Conclusion
There are dozens of parallels that can be drawn between the two institutions. It isn't surprising, given how much they have intertwined over the years. Today, they are the new religion of man. Each nation has its own sect, but they are all effectively the same & equally dangerous.