Meaningful Dialogue Impossible with Religion?

I have been going back and forth on my opinion of religion lately.  Fundamentalism bothers me, but I am a big fan of free speech, so I guess the religious should have their say as well.  Cencorship, even of falsehood, seems criminal to me. 
I think I just hit upon one of the major problems with religion in the public square.

To make the right decision as a group, a good way to go is to spend time discussing options and weighing outcomes.  Open discussion is huge: even if I have a great idea, you might point out a flaw in this idea and we'll have to further plan before we proceed.  Once we've discussed thouroughly, we can put it to a vote.  If the vote is divisive enough, we can discuss and vote on compromise.
This is supposed to be the idea behind democracy, right?  And I think sometimes it actually happens this way.

But when you put stubborn dogmatism into the mix, everything breaks down.  Dialogue is impossible with fundamentalists, because they will not even listen to the opposing viewpoint:

"Hey, don't you think we should let same-sex couples marry?"
"No!  Person X, who I believe speaks for god, says that that is wrong and evil and terrible and an attack on the institution of marriage, which GOD INVENTED."
"I understand your point of view.  But consider-"
"No!"
"Well I thought if we could discuss-"
"No!"
"Perhaps then, if we can never agree on this matter, we could compro-"
"No! NO! NO! NO!"

This is not dialogue.
I am aware that there are many things that destroy dialogue in this way.  Even stubborn atheism might.  Opinions are okay, and values are okay, and worldviews are okay, but in a society which is populated by a variety of people, we can't afford not to have meaningful dialogue and open, honest exchange of ideas.

Still, it seems like religion really does this a lot.  Like when a church leader says that atheists are only rabidly fighting the level-headed Christians because they are sinning and can't face their own indecency.
...ahem...
A.  I'm behaving quite well, even by your standards. 
B.  That is ad hominem, and has absolutely no relevance to the discussion at hand.
C.  I'm willing to discuss things calmly with you, but you keep shouting me down.


So I guess I can't, through this line of reasoning, condemn open-minded religion, if there is such a thing.

I'd like to discuss my philosophical questions with people around me, but they're all LDS, and after a certain point discussion breaks down.  Usually it ends up with them saying "I feel sorry for you."
I hate that line.  I said something similar to a friend once in high school, and he angrily called it "unwarranted pity."  That has stuck with me.
The thing is, "I feel sorry for you" means "you obviously don't understand, are too pigheaded to understand, and I pity you for not being as humble and enlightened as I am."
Discussion over.  It's like playing tic-tac-toe, but the fundamentalist gets to place as many Xs as she wants, and I only get to place one O.  I can't win, not because of my strategy, not because of my mental capacities, but because the outcome is already decided by the other party's unwillingness to play by any rules that make the game a game at all.