I think the former may require the latter. I’m not sure how an atheistic (in the literal sense) population could resist the forces of selfishness and tribalism over generations (again, this isn’t to say that religious people are unwavering, but I think religion does function as an anchor that keeps a population’s mores from drifting too far). As for whether most non religious people are moral relativists, perhaps they aren’t individually because they’ve settled on a morality that is palatable to them, but in aggregate I posit their morality (moralities?) drift more readily than religious persons.
And as a reminder, this is all speculation and I completely understand that you may not agree (I may not agree by the end of this thread!).