The trouble with that is that for a lot of people's intuitions, it seems that fairness not only permits but actually requires setting aside property rights. I'm not sure having a conflict between two interpretations of a basic moral value fits into Haidt's ideas; he seems more focused on conflicts between two different basic moral values.

Of course, you can take respecting other people's property rights as avoidance of harm. That might be a better fit. But then you have the opposed view that to retain your property when it could be taken from you and given to someone poorer is to harm the poor person.

I think the categories would really be simpler if "mine and thine" were recognized as a basic category.