Having an open mind doesn't mean that one never comes to any convictions in life. It's possible to have an open mind and live a principled life, without holding one's beliefs dogmatically.
Having an open mind means being prepared to question even your most central beliefs if there's occasion to do so. It means being open, when the time comes, to having your mind changed by an argument better than one's own.
It means being able to think both sides of an issue. It means being able to suspend your beliefs, to play devil's advocate, and to detach yourself somewhat from your own beliefs, actions and feelings. Only living with an open mind gives us a chance to grow and change.