Usage note, in that context "had" expresses, "If he had common sense (i.e., is known to have common sense), and still has common sense, then he wouldn't do that". For example,
Max: I'm going to give away all my money and possessions to the people in New Orleans who lost everything.
Pat: A man who had common sense wouldn't do that. Max, let's think about this for a moment, because I know you're a man who
has common sense. If you gave away everything you owned, you'd be just like the people in New Orleans who lost everything. Why not rethink it? What about denoting some money and some of your clothes and furniture? That's what a man like you, one who
has common sense, would do.
If Pat uses
Present "has", it would imply that Max doesn't have common sense:
Max: I'm going to give all my money and possessions away to the people in New Orleans who lost everything.
Pat:
A man who has common sense would not do that.
Max: Are you saying I don't have common sense?!