Robert Bellah's last major work (as he says - he is in his eighties), Religion in Human Evolution, was designed to show that the world religions that emerged in the "axial age" around 500 BCE grew out of parallel social evolution. The new, very hierarchical and often brutal states of that era produced a reaction of "renouncers" - mostly traveling teachers who criticized the current state in the name of a perfect standard located in the past or in another plane beyond this one. This is an interesting story. The sociology seems very plausible to me. I was a little disappointed that there doesn't seem to be much religion left in his discussion of religion once he has extracted the philosophy he was looking for, but that might be a story for someone else to develop.
Bellah then tries to tie this moment of social and intellectual evolution to the larger framework of biological evolution. The link between them is that playing, which animals and early humans did, led to singing and dancing and rituals. The rituals, which still partly endure, became the basis of religion and of social solidarity - a very Durkheimian thought. The evolutionary connection between play and ritual is, he admits, a late addition to the book. In fact, he barely mentions play through the whole core, where he compares the various axial age proto-philosophers. Still, I can see how this might be true. Worth someone investigating.
Then Bellah starts going off the rails. He says that just because the world religions evolved from earlier tribal religions, and from animal play, doesn't mean they are better or true. He wants to avoid judging any religious metanarrative from the perspective of another religious metanarrative. So instead he judges them from the metanarrative of evolution, on the grounds that evolution is the only metanarrative believed by nearly all thinking people.
And then I think he gets himself into a real tangle. On the one hand, he says that there is no standard, not even evolution, from which to choose among the religions. On the other hand, he extracts from all of them an "axial ethic" of universal equality. Moreover, he says that that the axial thinkers were utopians, but it would be unreasonable to try to make more than modest social reforms based on their ideas. And while it would be improper for this book, which ends its story 2000 years ago, to comment on the subsequent evolution of religion, he does think “it is imperative that humans wake up to what is happening [to the environment] and
take the necessary dramatic steps that are so clearly needed but also at
present so clearly ignored by the powers of this earth.” He doesn't specify what those steps are, but the main culprit he names is the invention of agriculture.
Bellah's position, that the point of all the world's religions is universal equality in social ethics, and environmentalism is a quasi-religious imperative, sounds like just what you would expect a Berkeley sociology professor to believe. The outcome of religion in human evolution from the paleolithic to the axial age is mild reformist liberalism.