There’s a whole bunch of undefined terms that are being used differently here. So I’ll try to clarify my position (a little).

by “religious” I mean (roughly): a majority (maybe slim but 50% +1) has some kind of religious belief and a majority of those people make at least a minimal effort to practice something that might be called a religion.
by “areligious” I mean (roughly): a majority has no religious belief and/or a majority of those who do pronounce some religious belief make no effort to follow their supposed ‘faith’.

Cultural continuition sounds like a nice idea but does it really work in practice? The shakers tried it and look where they ended up.

I think the benefit of some kind of widespread shallow religious belief is not that it scares people into behaving well but that it helps stave off nihilism (for most people) and makes them think that continuing their way of life into the future is worthwhile and that helps them go through the difficulties and inconveniences of raising future generations. It’s not enough (there are very religious countries with low birth rates) but it can help.

I think countries learning to live with less populations is a good idea, but the elites (who actually set policy) don’t and are detrmined to bring in new warm bodies to take up what they see as the economic slack and don’t care if these new warm bodies are interested in continuing the culture of their host countries – and mostly they’re not. The old model of assimilatory immigration is mostly dead and immigration now mostly means population and cultural replacement.