The Reagan and Bush era is called in Balmer’s book, God in the White House, “Listing Right.” I’m not sure about the personal faith of either GHW Bush or Ronald Reagan, but it appears to me that both of them were willing to play the card Jimmy Carter played so well:

The faith card.
Now: a sensitive topic for me, but one I’d like to learn from in conversation. How genuine do you think the faith card is for our political candidates? Avoid words like hypocrisy, jerk, disingenuous … and instead stick to some facts, appointments, decisions, etc.. What do you think? Do you think the entrance of religious rhetoric into the campaign, especially since Carter, has been good or bad?
Jimmy Carter announced he was a born-again Christian and, though I think he was then more born-again than he is now, his Christian commitments have always been to the front of his statements. He is now a moderate-to-liberal Southern Baptist. As we write this there are plans for the New Baptist Covenant surrounding Carter.
But what about Reagan and GHW Bush? Here are some of Balmer’s conclusions:
Reagan experienced a born-again conversion as a child at a Disciples of Christ church; went to a Disciples college (Eureka). These are credible faith elements of his journey to the Presidency. Reagan attracted the conservative evangelical vote in spite of his divorce and re-marriage (which today seems trivial compared to what Balmer had been the status quo — which in my own experience is about the time the evangelical movement became more tolerant of divorce and remarriage) and in spite of the fact that he and Nancy rarely attended church and in spite of the fact that Nancy consulted an astrologer.
Balmer is keen also to show that the Reagan’s own decisions, in spite of appointing some clear evangelicals (Koop, Watts), did not follow through on the expectations of the Religious Right. Balmer has some telling quotes from Paul Weyrich to this effect.
GHW Bush is known for having switched from campaigning against Reagan, where he differed both on abortion and on Reagan’s “voodoo politics,” to becoming his right-hand man as VP. Part of this switch involved Bush being more vocal about his faith. Bush surrounded himself with conservative evangelicals.
Balmer concludes this chp with a reflection on the need for a common enemy for a movement to gain strength — when the Iron Curtain collapsed there was the need to find a new enemy. Enter Clinton and Bush.