Trust is contextual. If I am a quarterback, I need to trust that my left guard will protect my blind side from the monster of a defensive end glaring at me across the line of scrimmage. He may be an asshole, treat women poorly, or have other character flaws, but if he does his job on the field, then I trust him in that context.
Leadership teams are really a composition of managers who, first and foremost, need to do their jobs well. That includes working in synchrony with their teammates and making sure their functional areas work in synchrony with other functions. Instead, many managers create their own little (or big) fiefdoms that compete with other fiefdoms in the organization. It’s like the offensive coordinator, offensive line coach, receivers coach, and quarterbacks coach each having their own, competing agendas. Now, what kind of football team would you have then?