When I don't believe I can learn something and I don't find it interesting I try to get to why this person believes what they say and why. If they have logic or if it is emotional. My goal is not to argue or convince but rather understand. This will help me communicate with them.
It is sometimes VERY hard for me to do this because of how I'm wired but I think working on this makes me a better person. I have given up on arguing and trying to convince people. Especially those that do not use logic or reason. And this is most people I have met. In my experience most people live in emotion not reason and thought. I think this is getting worse rather than better for many reasons.