Although such ideas are generally claimed to be consistent with
evolutionary theory, they conflict with current understanding. Even the
postulate "Morality should be based on the principle that everyone should
promote his own evolutionary success" is a philosophical premise, not
scientific, just as "I have a moral obligation to drop things or knock them
down" is not derived from the laws of gravity.
"Everyone should promote his own evolutionary success" does not provide
much guidance. This is popular until one realizes that it applies to other
people, too. "I can do as I please" runs into trouble when what pleases
someone else displeases me. Instead, most purportedly evolutionary moral
philosophies are "Everyone can do as I please". This is not in the
evolutionary interest of most other people. Racism, for example, if
successful, would promote the success of one group at the expense of
another and so might work as an evolutionary strategy. However, what's
sauce for the goose is sauce for the gander, or, in this case, for the
duck. It would work just as well for the Jews to exterminate Germans as it
would for the Germans to exterminate Jews.
On the other hand, if we base our morality on something better, such as the
Bible, biological insights can still be helpful in applying the precepts.
E.g., being fallen, we tend to pick the wrong way of doing things. Given
the evolutionary heritage of the importance of reproduction, sexual sin is
likely to be a particular problem.