There's an old saying that "culture is religion externalized." This is a simple way of saying that by looking at the culture a society creates and consumes, a person can discern, in general, that society's basic beliefs and worldview. "Worldview" refers to the major philosophical questions of life which influence our outlook on life, such as: Does life have meaning?, Is there a god and is he/she/it involved with the world or separate from it?, What responsibility, if any, do I have to other human beings?, etc.
As Christian philosopher R.J. Rushdoony explains:
Every culture is a religion externalized, a faith incarnated into life and action. The mainspring of every culture is its basic faith, its religious beliefs which undergird its hopes, action, and perspective.
Examining culture to learn about beliefs is a common practice. For instance, historians examine the Epic of Gilgamesh to learn how religion affected ancient Mesopotamia. From Gilgamesh, one can intuit that the Mesopotamians did not believe immortality was generally attainable by humans, because Gilgamesh sets out on a quest for immortality but eventually realizes humans can only achieve immortality through accomplishing "great actions" on earth.
Religious beliefs influence culture in a variety of ways. Certainly before societies were as civilized as ours, religious beliefs and culture were much more effectively mixed.
Today, religious beliefs help determine the value systems used in a culture. In America, many of the regulations and laws are based on concepts and priciples articulated in the Bible. This makes great sense because Puritans helped build our great learning institutions like Harvard and Yale. These priciples set forth acceptable behaviors and necessary consequences for breaking them. These similarly align to the Ten Commandments in the bible.
Another way religious beliefs influence cultures has to do with service to others. In our own selfishness, we easily turn inward and focus on the self, not society. Religious groups help to foster community, giving, and fellowship. Having common beliefs puts people in accountable relationships. Research has even demonstrated that participants in churches, regardless of denomination or sect, live happier and longer lives.
Religious beliefs often unify people in a culture. Coming together for meals, listening to the same music that identifies a religious belief, and practicing the same methods of worship gives people a shared identity.
Religion gives order to our perceptions of the world around us, and, in this, functions as a microcosm of culture in general. Although religion does not serve as widely to shape our group identity as culture, it is the single most influential factor in defining and reinforcing group norms. Societies that are deeply religious tend to demonstrate wider cultural homogeneity than those where religious officials, churches, and believers exert less influence. This paradigm is shifting in the modern era, as culture and religion both become more globalized and the politics of diversity and multiplicity become more valued.
However, many of the rites of passage which define cultural practices-- birth, coming of age, marriage, education, aging, and death-- are still heavily rooted in religious tradition and are, arguably, what truly defines our collective consciousness in terms of cultural ritual.