What's damaging about moralizing that we wish to avoid, what useful purpose does moralizing usually serve, and what allows to avoid the damage while retaining the usefulness? It engages psychological adaptations that promote conflict (by playing on social status), which are unpleasant to experience and can lead to undesirable consequences in the long run (such as feeling systematically uncomfortable interacting with a person, and so not being able to live or work or be friends with them). It serves the purpose of imprinting your values, which you feel to be right, on the people you interact with. Consequentialist elucidation of reasons for approving or disapproving of a given policy (virtue) is an effective persuasion technique if your values are actually right (for the people you try to confer them on), and it doesn't engage the same parts of your brain that make moralizing undesirable.
What happens here is transfer of responsibility for important tasks from the imperfect machinery that historically used to manage them (with systematic problems in any given context that humans but not evolution can notice), to explicit reasoning.
Taking advantage of this requires including those tasks in the scope of things that can be reasoned about (instead of ignoring them as not falling into your area of expertise; for example flinching from reasoning about normative questions or intuition as "not scientific", or "not objective"), and developing enough understanding to actually do better than the original heuristics (in some cases by not ignoring what they say), making your explicit reasoning worth trusting.
This calls for identifying other examples of problematic modes of reasoning that engage crude psychological adaptations, and developing techniques for doing better (and making sure they are actually better before trusting them). These examples come to mind: rational argument (don't use as arguments things that you expect other person disagrees with, seek a path where every step will be accepted), allocation of responsibility (don't leave it to unvoiced tendencies to do things, discuss effort and motivation explicitly), development of emotional associations with a given situation/person/thought (take it in your own hands, explicitly train your emotion to be what you prefer it to be, to the extent possible), learning of facts (don't rely on the stupid memory mechanisms which don't understand commands like "this is really important, remember it", use spaced repetition systems).
And the list goes on. What other cognitive tools can significantly benefit from transferring them to explicit reasoning? Should there be a list of problems and solutions? Which unsolved problems on such a list are particularly worth working on? Which problems with known solutions should be fixed (in any given person) as soon as possible? How do we better facilitate training?