Personally, I believe it is possible, but only if both parties are actually interested in understanding the reasons why the other feels, believes, and speaks a certain way about things. I can understand something but not agree with it. The problem is that there are individuals on both sides who will claim that your disagreement is simply a sign of your lack of intelligence or ability to think rationally and logically.
No one wants to admit that two people can go through identical experiences and come out with entirely different conclusions about the cause and effect of said experience. Of course, you see it most often here in the religion forums. One person expresses a differing view from another, and immediately the other creates a completely fictional biography of the one who disagrees, calls it fact, and then attacks the beliefs that the person who disagrees hasn't even expressed.
It's possible only if both parties are interested in listening and learning - not just in being right. That's my take on it. I'm sure you'll get a good deal of feedback on this one! :)