Why do people vote against their economic interests? Take a look at some threads here.

[loyalsister]

10. In my experience

It has been "God, Guns, and Gays."

To that I say that it's time to let go of the guns issue as it has been decided. As an atheist I have begun to make a distinct effort to acknowledge value in whatever gets a person through the night. I usually point out that I don't know a lot about it because I haven't read the bible and I am not inclined to. It makes it easy to end the conversation civilly. If I have serious problems with it, I walk away. No minds will be changed they are worthless conversations.
When it comes to gay marriage and gay rights, despite living in a mostly red state, I don't find myself mixing with people who oppose them. Abortion is another story. When it comes to those I try to get out of that conversation with some kind of vague agree to disagree language.

If we are part of campaigns, the main thing is to operate on an assumption that they have come to their conclusions based on their upbringing, cultural experience, and education and that they have value.
It's not my goal or business to change it.
I think developing relationships with people who vote against their interests is possible if show at least some respect for at least some of their beliefs and lifestyles. When it comes to social issues that have real widespread effects we have to stay out of those woods and focus on things that have effected their lives positively.

We should use some of the strategies we see politicos using with talking heads - deflect, dismiss, redirect, etc. in conversations. And especially keep it positive and personal.