We only need history to prove this. Every time a religion, mainly Christianity, has been corrupted, it led to absurd rules of oppression and terror(such as the Crusades and the witch hunts), and most often leads to bloodshed. A corrupt government on the other hand will only do things for money, and most likely in the shadows. The impact of a corrupt government is much less meaningful than a corrupt religion.
People are more likely to obey and listen to a religion rather than our government, and because of the threat of punishment by "God" they fear religion more. This gives it a great chance to corrupt the minds of the people, and it already has.
However with government the people have a better chance of seeing holes in it, even though there are more holes in religion. People often times hate their government even though they are an actual threat to their person. Not only that, but people are willing to die and kill people for religion, but not for government.
Religion has the ability to make a large group of people do anything if they're dedicated enough, and I honestly think a religion could easily overthrow a government.
Aside from the fact that Christianity alone has run so many political systems throughout history, its influences are so deeply rooted history and politics, it is absolutely insane to think that one government would be able to stop it. Pew Research center estimates that 6.9 billion people out of the 7-something billion on Earth belong to some faith. If that many people are willing to die and/or kill others for it then that is far too many for any government (corrupt or not) to suppress. Corrupt religions could (and many argue do) rule the world.
This is essentially an argument between mass mind control and a corrupted group of people running a nation. I think everyone can agree that mind control is by far worse. The govt. We can stop, over turn, revolt against. Yes, lives would be lost but the overruling population of citizens would prevail. However, a mass population doing as their 'god' told them could lead to anything, people would theoretically be committing enormous accounts of horrid acts on one another.
Religion is something that goes so deep within someones mind that it often blinds one of logic. For example, the Catholic church committed countless atrocities in the middle ages, yet it still took hundred of years for people to start to think on their own. People are less attached to governments; Never in history has their been a massive revolution against a religious institution while corrupt governments always end up being replaced one way or another.
Communism (just one example of a corrupt government) managed to murder more people in a brief period in the 20th century than religions killed in the whole of human history, and probably by orders of magnitude.
Indeed the defining characteristic of Communism is that it rejects religion and makes it illegal. Essentially all religions hold that murder is wrong. Getting rid of religion was an essentially step in murdering 100 million people because in virtually any religion, that kind of murder is really, really bad.
Even in religious context, people who have power and authority can corrupted. As a Christian I've heard of a few cases where priests and pastors have embezzled church funds.
Some systems of government are very religious based. The dangers of corruption is such regimes lay mostly in government power, not religious power.
Here's why: police and military are usually under government control, not religious control. Corrupt dictators have often used secret police, or declared themselves commander of the armed forces
Mostly, corrupt leaders have direct access to their countries coffers. Some of the more brutal ones have use the military, or secret police, or torturous prison camps to get rid of anyone who opposed them, or otherwise didn't fall in line. In most of these cases, the death toll reached tens of millions.
It is currently legal in most countries to kill innocent people in mass murders(abortion), mess up the gender balance with transgender operations, discriminate against whites and men, etc. It is extremely rare for a religion to do so, despite all the nonsense people say about religion causing societal problems all the time.
Unless the religion also controls the government, it's corruption can only affect those who follow it. Those who don't believe in the religion mostly unaffected by it.
The government plays a part in everyone of it citizens lives. They control outright or through laws, policies, and taxes everything important. That being energy, health, transportation to name a few. The government controls your very freedom by creating laws and controlling the police and military forces. This give them the ability to incarcerate or depending on the government execute you. The only way to get away from a corrupt government is to rebel or leave the country.
That makes corrupt government much much more dangerous than a corrupt religion. And if the corrupt religion control the government, the citizens are truly (no pun intended) in hell.
Many times, no matter how corrupt the religion is, it is the result of corruption in the government. Think of the King James Translation of the Bible, it was completely based on political power and control over the people and not what the original manuscripts actually said. Think of anything the Catholic church has done that was corrupt, completely as a result of the theocracy it created, before church and state were separate. Yes, corrupt religion can act independently of a fair government, and can do horrible things on its own, but historically, corruption in religion has been in search of political and societal standing and glory resulting from corrupt government.
Even corrupted religion means nothing without control. A totalitarian regime controls all, giving it more destructive potential. A government can be corrupt and have any ideology. Regardless of the ideology or agenda, if it's willing to slaughter millions for that agenda then it's dangerous. Religion corrupted only has the intent (if this corrupted religion even has the intent of seizing power) and not the means. If it did seize power then it'd fall under the category of a corrupt government.
Let's take a look at the great country of North Korea. A country in which all of it's citizens are in a way, held hostage and brainwashed. These people are forced to think a certain way, act a certain way, and believe certain lies which may seem obviously ridiculous to outsiders, but are widely defended throughout the country.
This is just an example of a totalitarian government. A government in full control of ever citizens lives. A government that can decide what religion you practice, and kill you for doing otherwise.
It gets worse. A corrupt religion does not have nuclear weapons. A corrupt government does.