Belief should be only one of the building blocks of culture. Factual proof, gained over time, through experience, training or study, constitutes much of a societal culture that intends to survive for a time.
Belief serves a society when proof is not available in the explaining of matters. Belief is a powerful tool for social engineering, where the people are redirected in their activities for various reasons, including the gaining and consolidation of wealth and power.
A society which uses belief, rather than truth and proof, as the sole component of its culture, will eventually be led to engage in behaviors that are so deviant and destabilizing that the people who make up that society will eventually revolt or die for lack of a better culture. Culture has to include components that are based in proved methods for enhancing survival, maintaining voluntary order and social stability, and even allowing better and more functional beliefs to be heard. Beliefs are easily challenged in an ever changing natural world and environment.
Culture contains the codified and enforced versions of successful common wisdom, historical fact, proven methods, and the best alternatives in behavior, work and thought that leads to stability, prosperity and survival. Matters of speech, manners, and formalized ways of interacting that have proven to be successful in easing disputes, as they become "the right way" to do things.
Matters of faith and belief have formalized and codified ways of conduct. Successful societies have incorporated all of these and other elements of culture which, for most of the members, are acceptable and do not lead to deviation, destabilization and revolt.
There are definitive ideas as to what constitutes "deviance" in all of the building blocks of culture. "Deviance" can mean variance in behavior, belief and thought, from the norm that is accepted by the vast majority of the members of a society. The term can also apply to destructive, unethical, immoral, or other negative paths that are taken when attempting to change a society or to change the culture of a society.
Social engineering that is aimed at changing culture, but which is based solely on beliefs about great matters of importance, is a very volatile process. Unintended and even catastrophic consequences are highly likely, as others challenge those beliefs and offer better alternatives to the desired change in society.
That is why all components of culture should serve to complete the whole of a stable, successful society.