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Eliezer_Yudkowsky comments on Single Point of Moral Failure - Less Wrong
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A hypothesis which is non-falsifiable has an alternative which is also non-falsifiable. You don't get to "not worry about it" unless you can show that the prior is low, which is a separate matter from any difficulties of setting up an experiment that everyone will agree is definitive.
The prior has several parts. Would the null hypothesis be that people are moral because there are practical and emotional advantages? That the good effects of religion don't fade?
And just to go sideways a little, should "religion" be viewed as a single thing for this discussion, or do some religions or some approaches to religion have different moral effects?
Agreed, falsifiability isn't the issue. But there is a problem with the question being ill-defined. Questions such as "Does atheism make society less moral?" have to be unpacked using counterfactuals, which in turn can be unpacked only if you have some precise conception of the alternative scenarios within some robust theory. These are missing in all discussions of these questions that I've seen.