Is there anyone who actually believes in moral darwinism under that self-description, or is it just a straw man position that people like to claim as the underpinning of the ideology of people they don't like? When I tried to google the term I found the book Moral Darwinism: How We Became Hedonists which is described thusly in a five star review:

Wiker tells the engrossing story of the centuries-long contest between Epicureanism and Christianity, with the Epicureans finally winning their long battle to impose their philosophy on science and the cultural definition of "knowledge." Exploiting the authority of science, Epicureans were able to seize the high moral and intellectual ground for agnosticism and materialism,thereby demoting Christianity from its prior intellectual prominence into the marginalized status it now occupies in the intellectual and university world. The Epicurean objective always has been and remains to achieve a moral objective by effectively banning the supernatural from reality, and with it any fear of judgment after death. Attaining this objective prepared the way for all the events we associate with the 1960s. Ben Wiker's intellectual history tells us far more than any scientific book could of the purpose and effect of the long campaign to establish materialism as the governing philosophy of the world. I highly recommend it.