I suppose that part of the issue is that I speak with such conviction that it often seems to others that there is no way that I will change my mind about whichever stance that I have taken. This is particularly frustrating for those whose stance happens to oppose mine. It would probably surprise many who know me to find out that it certainly is possible to change my mind about a great number of things. In fact, I am actually concerned about how susceptible I am to other people's opinions and ideas.
Let me use The Phantom Menace as an example. I saw that movie multiple times in the theater. Sure, Jar Jar bothered me, as well as Anakin's age, but the Darth Maul fight scene is still one of my all-time favorite lightsaber battles. Just the opening reveal that it was a -gasp- twin-bladed lightsaber gave me chills. However, the more that people talked about it, especially people I knew, the more that my views cemented into the negative. Nor is this the only movie that this has happened.
This also happened with music. I love Michael W. Smith's albums. Since he was a Christian rock star, there were few limitations placed on us listening to his music when I was growing up. I loved the music; I loved the message. However, one of my friends didn't care for the songs when I played them for him. He said that Michael W. Smith sounded constipated (severely strained) while singing. Despite still listening to his music, I cannot unhear that strain in his voice.
Even more important areas of my personal beliefs fall under this sort of influence. I can certainly be swayed by verifiable evidence (e.g. my view on wind turbines has taken a significantly negative turn in the past month). Also, poorly veiled propaganda tends to send me in the opposite direction of its intent.
I guess that I'm saying that, should you want to change my mind about something, it is possible. You are going to need to back it with solid evidence and avoid going for cheap appeals to pathos. However, I might look at you like you're stupid until you actually convince me.