One philosopher and blogger that I know has indicated that he now will accept friend requests on Facebook only from those who share his conservative political views. Liberals, he says, are anti-logic and inaccessible to reason.
On the other hand, if conservatism is true, it isn't the conservatives who stand in need of persuading.
I suppose you could take that attitude on either side of the political spectrum, or the religious spectrum for that matter. On religious questions, sometimes Christians bring out Rom. 1: 18-20 to explain nonbelief.
18 The wrath of God is being revealed from heaven against all the godlessness and wickedness of people, who suppress the truth by their wickedness, 19 since what may be known about God is plain to them, because God has made it plain to them. 20 For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.
This may be true, but bringing this up to an atheist leaves you with the job of proving that it is so. Just asserting it does nothing and accomplishes less.
At the same time I have seen atheists, under the influence of the new atheists, go from fostering real discussion between themselves and believers to treating them as if they cannot be reasoned with. John Loftus is who I have in mind here.
C. S. Lewis founded the Oxford Socratic Club on the idea that Christians should open a dialogue with those who don't believe and have real discussions. In politics, I don't think American democracy can survive the conviction that the other side can't be reasoned with. Nor can it survive the widespread belief that the other side is so evil that anything done to support one's own side is OK, since the alternative is, well, the eeevil other side.