There are things that are moral and immoral by any secular accounting. Those religious people say they'd reduce their (secularly approved) moral behaviour and increase their (deemed) immoral behaviour if they lost their faith. After that, it's just a question of whether you believe them.
This is simply not what was claimed. warpus said people identify religion as their source of morality, not that they
specifically claim that without religion they'd become immoral. They are separate claims, indeed, separate entire trains of thought, and should be regarded as such. For instance, if you suppose that the only reason some doesn't murder people is because god told him not to, that's not to suggest that he'd suddenly be OK with that sort of behavior if it was proven to him, beyond the shadow of a doubt, that god didn't exist after all,
even if that was what convinced him in the first place. It's part of his morality now. I could be wrong on this, but it hasn't been demonstratively proven in either direction, hence why I take umbrage at warpus' unsubstantiated claims.
What you're hemming and hawwing about "deemed" moral/immorality is also, I think, somewhat besides the point. The entire mental exercise is whether or not people would govern
themselves with moral precepts sans religion. I don't think we have to draw a line in the sand between so-called secular and religious moral teachings at all. warpus' claim amounts to the insinuation that people would not govern themselves with moral precepts without religion
OR if they had religion, and then lost it, more often than not would
stop governing themselves with moral precepts without religion, such that the "total morality" (???) would drop. Nowhere do we need to bring "Christianity vs. Secularism" into this, although I'll happily play that game if it's asked of me.
Their behaviour if they 'lost' their faith is going to be different than if they 'never had their faith' in the first place. They can only self-report on their losing of the faith. And, on that front, self-report is not a bad estimation - there will be (at least) a correlation. To judge people's morality sans faith would require an actual scientific study with people deliberately (and randomly) slotted into being given a faith or not.
I understand the logic of what you're pushing but it's still undemonstrated. There will be (at least) a correlation, you say - well, maybe, but prove it, or explain why it must be so.
For my own part, let me hazard this point: since becoming more secular, western society hasn't apparently gotten much less moral. And I don't mean in terms of Absolute Morals which we can or should subscribe to, but in the sense that even our secular western society governs itself according to some shared moral precepts, despite the fact that we lack the same faith of our intellectual forebears. For what that's worth, anyway.
It could be that we have replaced the faith with a different kind of faith. Maybe. I'm not arguing theology. I'm just arguing against the idea that religion makes us better as people. It is a demeaning, misanthropic suggestion at its core.