Dealing with closed-minded people, or I should say, trying to have an open debate with anyone closed minded, is simply a task that cannot be accomplished. Religion is an example of closed-mindedness. So is atheism. You can talk until you are blue in the face to a Christian to try and convince them of other explanations beyond the Bible, and they are as good as a child with their fingers in their ears chanting "na, na, na, na." Same goes for the atheist. Neither will hear the other's argument nor take any possibilities beyond what they believe to be true as an alternative.
Politics is this way as well. In many ways there are many scientists this way as well.
I say, it's not important to try and "deal" with a closed-minded person. It is better to simply be happy and feel relieved if you happen to be an open-minded person. It is a liberating gift.
Keep it in mind that the key to discovery is asking questions. If no one ever did the world would still be flat and the moon would still be made of cheese.