What is the term for an organization or social/political system rigidly governed by rules without any exceptions?
I think you're looking for the word "fascism" or "autocratic". Though for answering the question more details are required. So I give you some choices.
Autocratic: a system in which someone makes decisions and gives orders to people without asking them for their opinion.
fascism: a right-wing political system in which people’s lives are completely controlled by the state and no political opposition is allowed
dictatorial: a dictatorial government or ruler has complete power over a country
fundamentalism: a religious or political movement based on a literal interpretation of and strict adherence to doctrine, especially as a return to former principles
absolutism: a political system in which a ruler has complete power and authority
There are some other words that usually refer to special country or religion like tsarism, canonical, etc.
I can express what you want in a different way, but don't have a specific term for the system itself. I might say something like, "...that organization is governed by mandarins..."
The word "mandarin" is a synonym for bureaucrat that has a very unyielding and officious connotation. From Wikitionary,
mandarin /ˈmæn.dər.ɪn/ (n.)
(historical) A high government bureaucrat of the Chinese Empire.
A pedantic or elitist bureaucrat.
A pedantic senior person of influence in academia or literary circles, often used pejoratively.
I'm not a historian of any sort, but I think the term alludes to the huge role that the very rigidly structured civil service examinations played in Imperial China, and the vast powers those who passed those tests and eventually became officials in the government exercised.
This is probably stretching the definition a little but it works in its more generic sense.
1. pertaining to, established by, or conforming to a canon or canons.
4. a fundamental principle or general rule: the canons of good
To address your question, I suppose you could say "an overly-canonical government."
Whenever I run into systems of arbitrary rules that have absolutely no flexibility, I think of the innkeeper Procrustes and the associated adjective 'procrustean'. Procrustes had an inn with beds that were of a fixed size. If you were shorter than his bed, he would stretch you to fit and if you were too tall, he would cut off your feet. See more here: http://en.wikipedia.org/wiki/Procrustes