Theists as we all know, like to claim that religion is the source of morals, even perhaps the only source. But perhaps there is a little more to it worth thinking about.
All evolved properties vary between individuals. Some for example having poor eyesight, while some are blessed with really good eyesight but perhaps a poor sense of smell. And this is probably true of our morals as well. Things like attachment to honesty or empathy for others, probably vary greatly between individuals at a deep natural level. Then if you are one of the unlucky ones and your moral instincts are low, you will probably assume that everyone else's are too. Because it is hard to imagine, things that you can not feel yourself, being part of someone else. You will therefore probably have little trust in your fellow humans, and will probably think that their claims of moral feelings are also empty posturing. Because of course many of your own moral claims will be just that.
Would not such a person, then be exactly the sort of person who would most like to see external sources of morality imposed from without ? To think such a things as a god is needed to enforce moral codes, and to fear their fellow humans without that ? In short something like the old saying. “If it takes fear of god to keep you in line, then you are not a good person.” May translate as. If it takes the fear of god to keep “me” in line, then that must be true of everyone.
Is there therefore, a direct link between religiosity, and low moral feelings ? It always seems certainly true, that for example, religious apologists often use arguments that seem to be so dishonest, that you feel that most secular people would feel ashamed to pretend to such positions, however devoted to a cause.
It is perhaps too often said that religious people are not always stupid, or secular people more clever. ( Its debatable.) But could there be a natural difference in moral instincts ? Because if you have weak moral instincts, and little faith in them, then you will place that faith in religious codes ?
Morality comes from our societal structure as a whole and changes with the times. If morality came from someone's holy book it would be hard to explain differences in bathing suits from 1900 until present times. What would the religious say? That their god became more tolerant of us. Nonsense!
I think that morality comes from a complex of sources, from the societal structure yes, but also from heritage , animal instinct, economic forces and logic, plus probably quite a few more. Though at the bottom all of those it is driven by animal instinct, for without that as a driving force there would be no heritage, society, economy or reason to think logically. Humans would be no more moral than a clump of moss, even if it had a brain it could do nothing with it, without desires or fears.