The only reason we evolved as a species is through group/social cohesion. This is a bedrock of civilization that predates Christianity.
Discussion
Agreement upon common values is a good, general definition of religion.
The fact is that "do unto others what you would have them do unto you" is not a universal across history.
No values are completely universal. As I understand it, humans have socially evolved to hold to in group and out group distinctions. The rule of reciprocity is fundamental to in group social cohesion and predates Christianity as demonstrated below. Your claims are not substantiated by history and are religious dogma. 
https://en.m.wikipedia.org/wiki/Empathy
Read the sections on “Development” and “Genetics”
Just because they can be found many places doesn't make them non-religious. The cultures that tried to do away with religion also lost common goodness, implying the two are linked.