Dawkins is (and always was) a post-theist Christian
https://www.unqualified-reservations.org/2007/09/how-dawkins-got-pwned-part-1/
Many Christians see the modern decline and the semi-retraction of 'New Atheists' like Dawkins and want a more hardcore version of modern schismatic Christianity. As the preceding link makes clear, that would be a mistake. Dawkins represents exactly that form of Christianity, and adding cosmology will not vitiate his ethics.
Instead, Christian should re-embrace Scholasticism, making reason based on experience respectable within the Church
https://fvdb.wordpress.com/2010/04/20/the-duel-between-good-and-evil-aristotle-versus-plato-ayn-rand-versus-kant/
Dawkins himself should embrace the naturalistic ethics he highlights in his book The Selfish Gene, but rejects in favor of "rising above" our nature (to embrace a toxic form of ultra-altruistic Christianity)
https://en.wikipedia.org/wiki/The_Selfish_Gene