I thought it was well established that poor people generally prefer to vote democrat, so I think OP's question is really about why do any poor people vote republican. The answer in either case (whether voting dem or rep) as others have noted already boils down to economics 100%. Welfare and jobs essentially. So for e.g. in WV, it's rational for the poor folk to vote rep. By the time, religion and culture make it into decision making, i suspect we are no longer talking about the bottom layer.