I think honor concerns equates to concern for good reputation, and people strive to form the kind of reputation that their social group values (Barclay, 2015; Cottrell, Neuberg & Li, 2007).  People can form impressions of themselves that is inconsistent with what they believe in, especially if they think that it would reduce their chances to be seen as cooperators in that group, if they will be excluded, or if they will be harmed (e.g., if you are non-religious, you can seem like a religious person around religious people or hide any signs that may give away your true beliefs, and how much a person would be motivated to hide their true belief/values would depend on the costs). Also self-concepts are connected to reputations, and self-concepts can change to become more in line with a person's social image in time. There is evidence that certain aspects of morality are internalized, such as lying or harming someone. Many murderers (unless they are psychopaths) feel extreme anxiety even when noone knows that they killed a person. Over time, with successful impression management, their anxiety may reduce. People often are concerned with how others perceive them even when no immediate or future outcomes depend on the impressions they make (Leary & Kowalski, 1990). I am rambling, based on this research, I think certain aspects of honor concerns would be observed in completely private contexts too.