we're all in this together somehow . . .

I've not worked in adult literacy, but I have worked in situations where I was bringing services to people in vastly different social circumstances, and I think there's probably some commonality.  You're bringing them letters, and they're bringing you glimpses of an often scarier world.
It helps not to think of yourself as a teacher, and teaching, but to think of it more as sharing a skill.  Adults learn other stuff, and they may have some idea of how to learn that works for them, or you may have to help them with that.
There is a big difference between kids and adults in terms of motivation.  Adults learn things because they want to to, or because they see the need.  A good percentage of the people you'll be teaching were once kids who just didn't see the point, and had something "better" to do. 
I want to address the "it worked for me, but not for them" aspect.  Actually I almost want to ask "how did it work for you?", because despite the fact that I am one of the mildly over-educated, I can't really say that it worked for me the way I thought it was supposed to. 
In 1975 I went to Morocco as a western European teenager, coming from an educational system of superb repute.  At 18 had I read about political systems, philosophy, sciences, etc.  In Morocco I became friends with a kid my age who had never gone to school in his life, but spoke seven languages fluently, (some of them in more than one dialect), knew how to hot-wire a car, and was a fantastic pick-pocket.  As far a I can see, he had an edge on me in terms of survival skills.  In retrospect it seems that he also had a much keener understanding of political process and social realities. 
When you say that the system worked or works for you, you are basically saying that you've learned rules to exist within this particular system. To put it bluntly - you too got fucked by the system.  Perhaps you had metaphoric lube and it wasn't painful, but you are left with the erroneous idea that you're somehow safe because this system is working for you now.

As far as developing relationships - it will just happen.  As humans we form relationships.  Practical tools for developing relationships with people from different backgrounds are an openness of mind, basic respect for other beings, a willingness to disengage from one's absolute beliefs, and openness about one's own humanity with all it's failings. 
It takes a lot of compensatory skills to even survive in this system without being able to read, and it may be interesting to learn how your students do it.

That's a fair point. I guess I mean it worked for me in that it placed me into a high standing by society's standards. As in, stamp of approval. I'm doing fine. But I guess that just means I'm another well-running peg in the machine. It's a valid point which I think complicates the natural understanding of society. Is there a status quo for society's operation? When is society working and when is it not working?

In what ways does an illiterate adult work within the system and in what ways do I? Potentially, culture and familial relationships are more important to the illiterate adult. The way I feel detached from community might be as a result of my educational advancement. The adult however who has a harder time finding a job and making his way financially might be a core member of his own environment.

Learning then is situational. Maybe all I've learned is how to follow the rules. Maybe real intellect is twisting the rules to our own purposes.

I think there is a lot to think about in this...