That question can be taken in many different ways. One way is historical. I'm in no position to answer that question. Another would be sociological. I'm not in a position to answer that question, either. Part of the problem here is that I'm not an historian or sociologist. Another is that there's substantial vagueness in the phrase "religion as we know it".
Here's a different question I can answer: Does relgious faith have to be bound up with or somehow a consequence of one's fear of death? The answer to that question seems to me obviously to be "No". I suppose there are particular forms of religious faith that are so bound up with a fear of death, and perhaps these are the most visible in American public life or the most salient to non-believers, but there are plenty of forms of religious faith that are not.