It can and obviously is argued that things like the Golden Rule come from logical selfish thinking such as tit for tat or karma (what you do tends to come back on you) and so on.  I don't however notice that the proponents of things like the Golden Rule usually offer such reasoning as the reason we should follow them.  Instead they are offered as axioms of goodness, not something in our personal interest, and we do them out of a desire to do what is good.  Besides, often enough it is to our selfish advantage to not follow the Golden Rule, and even in society's rational advantage (such as punishing criminals, even though we would not want to be punished).

We also see examples of human kindness and generosity that goes way beyond anything that could earn reward for us -- saving beached whales, at great inconvenience and expense, or people dying (maybe or maybe not foolishly) for causes they perceive as greater than they, such as country or God.

It is in the modern "materialist" frame of mind to try to explain everything with some sort of selective advantage, including this amazingly widespread Golden Rule type of thinking, in spite of all the cultural differences from which such thinking derives.  The thing is the thinking does not come from ordinary people but from what we would call religious geniuses or saints or prophets or things like that, and then gets adopted by their followers because of its inherent rationality and appeal.  It took Jesus to introduce it into Abrahamic thinking, Buddha into Indian thinking, and so on.  (I rush to aver that similar thoughts can be found in the OT or in Hindu teaching -- again from limited sources).  Most of us are not born with the Golden Rule, we are born more selfish but with a desire to get praised.  We learn if we are able.

So I have trouble saying this is an evolved instinct.  It is I think instead a rational proposition derived by religious geniuses from their meditation or prayer or just reasoning that gets adopted quite widely because of its power, and biology is not involved.