Reputation: An Islamic Analysis

When someone engages in unbecoming behavior or sins openly in ways that Allah (swt) has prohibited and then boldly claims “only God can judge me”, what statement are they really making?

Even for those of us who seek to live righteous lives, is it really true that we should completely abandon the idea that our reputation among others matters? Does the prophetic tradition endorse this abandonment of maintaining a good reputation? Or is it possible that our reputations mean more to us than we realize?