All I've really got to say, is that whatever widely influences the masses of the population, the corrupt will find a way to use it to gain more power. Whether it's a catholic pope, a cult leader, an anti-religious communist dictator, or anything else, it's not about what they use to gain more power. A corrupt person, with the initiative to take power for themselves will use whatever means necessary. It's not a "Government and religion don't mix", it's more of a "government can be a real bitch". My personal philosophy, and what I have observed, is that the best leaders are the best followers. 

Governing bodies of any type and size will use what is popular appeal to the masses to influence them towards their own policies. Doesn't matter what it is.