So, first of all, morality is relative. There is no absolute 'good' or absolute 'bad.' There is not even 'more good' or 'more bad.' There is only empathy. Thus, some humans, feel the need to create a consistent moral framework anyways so there's a conflict between the idea of creating a 'framework of morality' and the belief that morality is relative. You can't organize something that doesn't have order. ..But does it really have no order though?
Emotion is extremely central to morality or our daily experiences of "good" or "bad." It is the only universal thing across moral philosophies. "Thou shall not hurt someone." Physical pain is not universal. Some cultures or individuals are ok with physical pain or even suicide. Emotional pain is. But, at the same time, what constitutes as emotional pain is relative. Certain actions towards other people are emotionally charged, some are not. (In most cases, a punch in the face is emotionally charged.) It's relative to the individual and it's relative to society, and it's relative to the relationship of the individual's emotions to society's rules. Emotion has both order and relativity at the same time.
So for a moral relativist that can't help but be empathetic, the way to deal with every individual is to figure out what triggers their emotions(usually it's relative to the rules of their society or the dominant moral constructs, and usually punching someone in the face or murdering them would be emotionally charged.). But really, the most logical thing would be developing information and knowledge. Information shapes emotions. Informed feelings are more...accurate than uninformed ones.
What do you think?