Customary meaning what every ethical philosophy has done. Even systems of thought like Pyrrhonism or Cyncism focused entirely on freedom from collective assumptions and social control, still have their own sense of 'good', and they take it not just seriously, but ponderously so. They survived on the basis of their moral core, and concentrated it over time. It seems unavoidable. But he thinks its usefulness has been exhausted.
Nietzsche seems to have been acknowledging the problem with post-modern thinking. The acceptance that any system of thought that wants to work is going to have to accept real falsehoods, paradoxes and inconsistencies and deal with them in subtle ways opens the door to absolute relativism and the utter abandonment of philosophical perspective.
It is hard to walk the line between what Nietzsche thinks of as courageous, challenging thinking, and utter nihilism, which can only take one backward and away from all challenges. That would ultimately be (or perhaps, by now has already been, depending on how you look at recent currents) harm.
In other works, there is an importance to maintaining 'taste' and associated refinement without letting it be a 'morality' that will base a social conscience, coalesce a 'herd' and run your life for you. This is something not very natural to humans.