Hi George. That's a tough question - and probably the one we never quite know the answer to with any certainty. It's one thing to decide intellectually that 'yes, it's a good thing to be open minded' and strive to be so. It's quite another to BE unthinkingly so regardless of what buttons get pressed in life situations.
It's perhaps a much bigger question than we realise too. There's good reason to think that the very fact that we find ourselves apparently existing in this reality (even if we do flit about the afterlife at times), and perceiving ourselves to be a personal self is proof that we're locked in by beliefs that don't take account of greater realities. i.e. that we are far from open.
The zen student in the old story who screams blue murder when his master starts strangling him after he announces he's supposedly transcended his fear of death comes to mind. 'So you don't fear death???'
Even 'open mindedness' gets misconstrued. Most of us can manage to be open enough to allow a (fairly - we still have our red buttons) free discussion of differing views. But it's another matter entirely to engage on a topic or in a situation without the range of acceptable options or outcomes being pre-determined by our personal view. At best we need time to fire up our intellect to realise 'oops, I'm supposed to be being open'.
This isn't likely to lead to an optimal solution, because as well as it risking our getting caught by situations requiring an instant response, there's also the issue that higher wisdom and seeing come not through intellectual analysis, but from the intuitive or heart side.
I quoted the Aesop's fable about the two monkeys squabbling over a piece of cheese in this regard yesterday. An old monkey offers to help by breaking it into even halves. This he sets out to do, but (surprise surprise) he ends up nibbling away at one piece to bring it down to size of the other. But overshoots, and so has to do likewise to the other - several times. Eventually the two go on their way happy with two equal pieces - being so focused on the other guy not getting ahead that they don't notice that the oldster ate most of their cheese.
Compromise is basically an ego driven and destructive process that inevitably results in sub-optimal solutions. This for example is the ultimate source of much of the lunacy that comes out of negotiated agreements, or politically correct policies, or bureaucracies. True openness requires the generosity and lack of selfishness to see, propose and permit the optimal solution in all situations - regardless of any personal view or interest getting into the mix
Perhaps the best we can hope for is to maintain as open an orientation as we can going forward - watching carefully for the ego sneaking in. We can only at a given time be what we are - this is the only place we can start from if we're not tp drift into self delusion....