First of all, I hope this post makes sense. I wrote this attempting to flesh out a few thoughts I've had running around in my head and just haven't been able to put into words until I read your post.
I think that what you're saying only applies to some people. From my experience, there are three types of people that I debate and argue with. All three originally hold opinions different from mine.
The first holds their viewpoints closely, but is open minded and interested in hearing more. They are willing to learn, and willing to listen. Continuing your metaphor, I would liken them to a student who, while having no clue what a partial derivative is, is actively (and this is the key difference from the second type of people) trying to learn the basics of algebra in order to reach a conclusion later.
The second kind of people I argue with are what I think you are talking about above. They are the students who are "so far removed from our conclusions" that they have no idea what's going on. They may resist the ideas we bring to them at first out of confusion, but they are still willing to learn, if not actively try to pursue more knowledge.
The third is the type of people I dislike debating and talking to. They are the few people I will give up on, that I refuse to waste my time on. They are the children who not only don't understand algebra and hence not calculus, but don't want to understand. They cover their ears and sing so they can't hear you. Many (if not most) even know that they might change their mind, but are so devoted to their own beliefs that they will actively work against understanding something.
For me, most of the time this plays out in religious debates. I'm a fairly unabashed atheist, and I often have friendly debates with people I know. Rarely do I ever encounter someone of the third type I described, but I know when I do. They are the ones who tell me I'm going to hell, who tell me my gay friends are going to hell, who tell me that the bible is the literal truth of god and the only thing that they will ever consider. They cut me off when I try to talk to them, they do everything possible to avoid even hearing any ideas that aren't there own. For those of you who are religious, I say this not to try to disparage your beliefs, but to describe a type of person I've encountered, as religion is my most common experience with them.
Sadly, I've also had the same problem when I've argued with MRAs and rape apologists who tell me that my best friends were stupid and probably deserved what they got. I've found the same problem with people who hate muslims and who talk about the "raghead" who runs this country. I've found the same problem when I talk to most any people with substantial bigotry. They do not listen, they do not care. I know you say that we often don't have the will to try and educate individuals "who on the surface are so repellant". It's hard to quit for me, but there are times I realize I am fighting a pointless fight.
I think that the first two types of people are people that we should talk to. Despite their "repellant" beliefs, at least I can talk to them. They constitute the majority of people, and they for the most part are willing to listen and learn. Despite the huge gap between beliefs, they are willing to help build the bridge between them. We can start building the foundation for them to understand our conclusions. They are willing to learn algebra in order to try to understand our fascination with calculus later on.
I think that's where our hope lies. I don't have a good answer as to whether we can really start building that foundation in places like the threads on DU, as it's hard to communicate often very complex ideas in such a small forum. But it's a start, and those willing to learn will pay attention. One post, one thread at a time, they will listen, and they will begin to understand. Often we will butt heads with those who disagree. In the recent GD "gender wars" threads, we will feel like we're not making any progress. But then someone will come along and say "hey, I never realized how bad this problem was before. But I'm listening, and I want you to know I'm on your side." They're the people that I work in my offline life to reach out to. Despite their initial resistance, I find common ground with them, and then try to explain my beliefs and thoughts from that point onwards. I agree; despite the challenge it presents, I will keep trying a little harder, and see what happens: in my experience, it's usually worth the effort.
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