I think the Dogs in the Vineyard is written so that, a) PCs should bear the consequences of their beliefs or choices, and b) the GM should push these consequences through escalation.
The problem with the game, as I see it, is that conflicts usually result in changing someone's opinion. Although it's possible to phrase conflicts in such a way that this does not happen, it's certainly a possibility that the rules do not discourage. And it's not often, in real life, that any discussion, however heated, results in someone changing their mind. They may have approached the debate undecided but actually changing their mind, very rarely.
Also, it's not uncommon for players to squeal after a conflict that they don't see why their PC should change its mind, although I've never heard such a complaint about an NPC.
There are a couple of ways of getting round this. You can either decree that PCs are unaffected by the stakes of a conflict. This is a bit dull as it might make PCs into superheroes but it could perhaps be run as competing demagogues trying to sway the opinion of crowds. The PCs could be the Politburo, rivals at the court of King Arthur or even members of a street gang. What's up for grabs is possibly control of the group, or at least control over the groups's ideas.
My favoured solution though is to extend this idea to all characters and decide that conflicts have no initial stake. Nothing will be changed as a result of a conflict that isn't changed through blows accepted in a conflict. This makes the conflict more natural, gives escalation more meaning and makes each blow much more important. You aren't just throwing in ideas to get those extra dice to win the stakes because there is no prize at the end.
And what happens if you give to some proposal? Nothing because argument never changed anything. Change must come through the barrel of a gun. Only the realisation of how far you want to push, or how far you have pushed, the conflict will change the mind of those involved. Not necessarily because they buy into your ideas, but because they are scared of the consequences of not joining in.