What is the dominate relationship between religion and social class in the United States?

The relationship is relationships. Each class needs the community that religion provides for different reasons. The wealthy need it for the business contacts and the reassurance of their own righteousness, regardless of what they actually do. The poor need it because they don't have much of a safety net beyond their friends and neighbors. And the middle class needs it because the likely alternative is being shut up in their suburban homes with very little neighborliness.

And, unfortunately, when you have someone in power who is of a particular religion, that person (regardless of his or her own moral worth and such) tends to get blind support from fellow followers. Take, for example, presidential elections; how many voters do you think vote for a particular person ONLY because of their professed beliefs?

I can tell you that here in Canada, Harper, who is a complete moron, got a lot of support from the 2 million + members of his evangelical church, solely because of his denomination - not because of his political platform. It's so wrong, it hurts to think about it.