Let's assume you understand the other's viewpoint. Through discussion, research, what have you, and you have a steel-man understanding of their position. That is to say, you can formulate the strongest possible case for their given opinion/position. Let's say that they also have a steel-man understanding of your position/opinion.
And you still disagree. You understand each other and still cannot find a common ground or consensus. What kind of value, if any, is there in continuing discussion at such a point?
There are several issues like this that come to mind with contemporary public policy in the United States, but I think that discussing this in the abstract is best.