Criminal Profile tracks how Jason and Lucia go about their work. It resembles the honor system in Red Dead Redemption 2, but Rockstar adds that it does not turn them into upstanding citizens.
The difference the studio names: crime that stays businesslike, set against violence there was no need for. The world responds to that reputation.
Unlike the Wanted level, the profile is not reset once the police lose you. Previews describe it as more than a good-versus-evil meter: repeated needless violence and chaos count against you, small decent acts count the other way, and violence during missions and planned robberies is weighed differently.
The Wanted system around it has changed too. It goes up to six stars again. Police work from descriptions of your appearance, clothing, and vehicle, a crime has to be reported before they respond in full, and hollow stars mean they have not identified you yet. Masks, a change of clothes, or a different car help you shake them.