To preface, the idea of religion evolving over an enormously long timespan is incompatible with the Judeo-Christian worldview. According to Genesis 1-3, religion started with the worship of the true God. However, man rejected God and worship degenerated into the worship of creation. God is Creator, not a product of evolution.
Secondly, there were no psychologists alive to even observe the behaviors of any alleged hominins.
Thirdly, no one seems to be discussing how atheism and naturalism evolved.
If religion developed gradually to meet various emotional or adaptive requirements for continued survival, then what brought about that need?
If our senses and intuition bring us into contact with reality, then would not religious belief connect us with God who actually exists?
Even if it could be proven that a few religions were the product of evolution, that would still not prove all religions had the same origin.