1. Religion as an element or aspect of culture.
What is the relationship of religion to culture?
Let me start by defining culture. By "culture" I mean a society's language, art, science, education, religion and its total symbolic system through which all its activities are expressed. Culture is a dimension of human social existence and the expression (the expressing and the expressed) of the meaning and values of a society. It is the "glue" or "bonds," that hold a society together, the raison d'être of a symbolic social order.
Religion is an element or aspect of culture. It is a system of expressions or beliefs of the ultimate or supreme meaning and value in a society, the measure of all other meanings and values. Religion is often expressed in stories and rituals. The stories are of beings, sometimes supernatural, responsible for the beginning and rescue of the society; and the rituals are reenactments of the acts of creation and salvation of the society. I think it a mistake to equate religion with a belief in supernatural entities, including God or gods. Moreover, if you define "God" as the "object of ultimate concern" (Tillich), then God, whether a supernatural entity or not, is omnipresent in human existence. Atheism, as Spinoza demonstrated, is merely the denial of God as a personified, supernatural entity, but not the denial of religion.
2. Morality and Religion
Is morality founded on religion? Is religion necessary for morality? In my definition, yes.
Morality is the system of mores or societal rules which determine correct or incorrect, good or bad, behavior. It is the behavior control mechanism of a society.
Culture (as I have posited before) is distinct, though inseparable, from economy and politics, the public and private tensions of our existence. If there is a social order, there is a culture. In fact we are recognizing that any social organization (e.g. a corporation, church, tenants association) has a culture which undergirds its goals and activities. Again culture is the dimension of human social existence that expresses its meaning and value: the answer to our question "why?," the objective of our desire to know.
Religion is the element or aspect of culture that expresses its foundational meaning and value. It is the predominant belief system of a culture underlying and motivating all its symbolic expressions, and the rules of correctness or incorrectness, blessing and taboo, for human behavior; that is, morality.
While morality is grounded in religion, an aspect of culture, it is not necessarily any particular religion, e.g. theistic or judeo-christian or any particular culture, e.g. western or eastern or indigenous or modern.
In Divinity School I read Richard Niebuhr' book, Christ and Culture, where he showed using Weberian "ideal types" the various role that Christianity has played vis-a-vis culture. This is helpful for understanding all religions and their relation to culture.