I think you might be misunderstanding the problem, it's not about disagreement, it's about a bullish refusal to admit that there might be any other perspective to a problem. It's not the disagreement that is the problem, it's the lack of respect for other posters.
People are entitled to keep their opinions. People don't have the right to demand that others see their side of things. They can argue that its one way or another, and other people can disagree. But, to call them out as disrespectful because they refuse to agree or acknowledge another POV, I think, isn't appropriate.
I have seen examples of responses to this and I do think they make the thread go downhill.
Catty comments like "but I guess nothing I say will change your mind..."
"it's obvious you just posted for validation because you are not admitting that you did anything wrong!"
Neither of those types of statements advance the discussion.
Another type of post that concerns me are the ones where people say "Why did you bother to post?"
These are all posts that turn the discussion onto the discussion. Instead of discussing the topic at hand, posters start discussing the discussion and their fellow posters and how they are discussing.
It turns it into a "meta" thread.
The rules have always been that if you have a problem with someone that you should take it to PM. I think that doing that or reporting the post to a moderator is much better than turning the thread in on itself.