Our native built-in moral code may be helpful for daily decisions within local social groups but there is little reason to think it functional when dealing with those outside our local social groups.
Your error is your continued insistence to lay the limitations of humanity on the doorstep of religion when in actual fact religion is a critical and perhaps primary mechanism for overcoming these limitations.
There is plenty of reason to think that it is functional outside of small groups. Every day I experience interactions with people with whom I do not share an in-group relationship, and yet I don't judge them as unreliable and those people don't judge me unreliable.
Religion does not help overcome these problems when they involve out groups. Religions are, by their nature, inward facing.
This is a deep topic and requires us to compare the prosociality of the religious versus that the non-religious.
There was a nice review article in SCIENCE on this by Ara Norezayna and Azim Shariff titled The Origin and Evolution of Religious Prosociality. I have linked to the PDF below.
https://static1.squarespace.com/static/52d7f47fe4b0c692d7426966/t/531e37c0e4b089910ebb95f3/1394489280903/the-origin-and-evolution-of-religious-prosociality.pdf Experimentally induced religious thoughts reduce rates of cheating and increase altruistic behavior among anonymous strangers. Experiments demonstrate an association between apparent profession of religious devotion and greater trust. Cross-cultural evidence suggests an association between the cultural presence of morally concerned deities and large group size in humans
I started looking at that paper and got distracted by another from the same authors:
https://www.sciencedaily.com/releases/2011/04/110420112334.htmTitle:
Different views of God may influence academic cheating
Date:
April 21, 2011
Source:
University of Oregon
Summary:
Belief in God doesn't deter a person from cheating on a test, unless that God is seen as a mean, punishing one, researchers say.
Ugh! In order to behave well, theists need to believe they will be punished? This again relates to our initial point of discussion, that some people primed for religion are those that need guidance -- and the threat of violence -- in order to act altruistically.