In his book, Start With Why, Simon Sinek describes a test, called the celery test, that is about being authentic and consistent. If you're at a grocery store getting food for your health food business, could someone look at your groceries at the checkout line and immediately know what you're all about? If you've purchased soy milk, chocolate, pudding, and celery the answer is no. If you're just purchasing the soy milk and celery, then yes.
The same is true about your actions as a professional. If you're telling your direct reports that the tone of meeting should be serious and that it's not appropriate to be light hearted, you probably shouldn't get up in the same meeting and tell a funny anecdote. If you're going to emphasize the importance of team work and say how much you value your team, you should also give them opportunities to provide feedback and really listen to it, even if you disagree.
If you're not passing the celery test, if you can't walk the walk after talking the talk, you've lost credibility and frankly damaged your integrity. People remember this kind of stuff, and if you want them to believe you, to think highly of your brand (whether individually or as a company) then you need remember that your actions need to be consistent with your espoused values. Sounds simple enough right?