The value system (and its underlying philosophical premises) which is being perpetuated by the society in which those areligious people live was crafted by religious tradition.

> Additionally, for most ordinary people over many of the thousands of years in question, participation in the dominant religion of the time and place was compulsory.

This is kind of a weird statement; for most of human history there was no line between religion and culture. So if participation in human culture is "compulsory" then I suppose you are technically correct, but then your statement is vacuously true.

Rites and aesthetics have existed independent of culture -- consider the Romans, who adopted, adapted, and incorporated others' rites but left the culture mostly unchanged. I don't know that the equivalence or dominance of religion-as-culture paradigm is conclusive.