Yup. This goes back to the Southern strategy which was brought to the fore by the Nixon campaign (although it was in play since before then). From that era we also get this chilling warning from Barry Goldwater:

Mark my word, if and when these preachers get control of the [Republican] party, and they’re sure trying to do so, it’s going to be a terrible damn problem. Frankly, these people frighten me. Politics and governing demand compromise. But these Christians believe they are acting in the name of God, so they can’t and won’t compromise. I know, I’ve tried to deal with them.