Judging the other person as "close-minded" automatically makes you "close-minded."
This is ego in action. This is you pulling the blindfold of ego more tightly over your spiritual eyes forcing you to view the world through the false perception of human eyes, rather than through the true light of spiritual eyes.
When you judge someone else, you are driving a wedge of separateness between you and them. The antidote to this is utter humility, combined with love, responsibility and perfect confidence (faith).
With this antidote, you can hear what the other person says with completely openness. You feel no contradiction or assault when there is no ego to make you into a victim.
This is not to say that whatever the person says should be taken as right or correct. It may not be, but ego is entirely removed from the equation and you have the patience and love of them in order to hear what they have to say.