The surrounding people don't need to be theist, but they need to use similar social tools to religion. Namely shame and reverence. Trying to "destigmatize" everything is one of the most destructive things the left has done to society.

Replace "sin" with "dishonor" and a society could be just as stable. But when the negative action stops causing any kind of stigma, both types would crumble.

You can have common doctrine, dogma, beliefs, and practices without the spiritual elements. Is that still a religion?