Consistency is not just about behaviours but also about systems, processes and procedures. If people are open to the idea of change, doing something differently, but for example, the admin systems or supplier arrangements or customer interfaces don't support the new way, then it'll be almost impossible to keep your people engaged in the new direction.
The most significant contributor to culture is the way people actually behave not necessarily what the 'rules' require. So consistent approaches by managers, all managers from top to bottom, is essential. That's where strong leadership becomes essential, to not only model the way but be prepared to make tough decisions about managers and others who by their behaviours, sabotage change initiatives.