An interview with Richard Dawkins in the New Scientist (21 September 2019) contains this exchange:
Graham Lawton: Another chapter in your book looks at progress in moral issues such as gender and racial equality, and you present a very upbeat picture. Do you worry that progress has gone into reverse?
Richard Dawkins: No. It's important to take the long view. I think there's absolutely no doubt that we're getting better as the centuries go by. The moral standards of a 21st century person are significantly different from those of a 20th century person.
Dawkins here seems to assume there are objective moral standards against which human moral opinions can be measured, i.e. moral realism. This surprised me because Dawkins is such a strong advocate for naturalism and it has always seemed obvious to me (including before I became a Christian) that naturalism is incompatible with moral realism — the famous is-ought gap. Sean Carroll, for example, has written about this much better than I could. In fact, Dawkins has apparently written (in River Out of Eden, quoted here):
The universe we observe has precisely the properties we should expect if there is at the bottom, no design, no purpose, no evil and no good.so unless he's changed his mind about that, it seems Dawkins at least professes to be a moral anti-realist.
This confusion illustrates why I've always found moral anti-realism so deeply unsatisfactory in real life. One can argue that there are no objective moral facts, and that moral claims simply express opinions shaped by evolution and culture etc, and even try to believe those things — but the temptation to think, speak and act as moral realists seems practically irresistible ... so much so that even the most prominent moral anti-realists consistently yield to it, and hardly anyone even notices.
Addendum Arguably the New Scientist quote could be interpreted in other ways, e.g. that by "getting better" Dawkins meant more internally consistent, or more in accordance with his personal subjective moral opinions. However I think it's obvious most people would interpret it as "objectively morally better" and thus if Dawkins meant something else, he needs to work a lot harder at eliminating such misleading language.