No, I don't think so. People like to think they have open minds - right up to the point that someone gouges a tender spot. Then the open mind snaps shut. Even when we listen to all sides, I think we can adapt new thinking to a point, but we do so without having a totally open mind. That new point must get with what we already believe. These are merely my thoughts. I haven't a clue as to a truely unbiased mind. I can only speak for my mind, and it is biased.
I think it is possible to have an open mind... not necessarily on every subject, but in general, it is possible. A truly unbiased mind would be an empty one... all of our experience, research and training create parameters in how we think about issues that come before us. However, if one is aware of these biases, and can withhold immediate judgement on an issue in order to consider other data, then an open mind is possible.
One has to consider biases in light of consequences also - as the initial judgement might be quite altered. If I give you a choice between $10 or $100 in cash... very few would opine that they have sufficient money that they would settle for the $10. But if it were qualified to say that you get $10 and the respect of your family OR $100 and lose a family member, it is judged in a whole different light.