I was talking with a friend of mine recently, Buddhist by philosophy, and he raised the question of when and how American Christianity became linked with conservatism, since until fairly recently in terms of history, it's been linked with liberalism and progressive thought, viz. abolition, women's suffrage, child labor laws, pacifism, opposition to capital punishment. (Overseas, in fact, it's still linked with liberalism.)
"Liberal" became a dirty word in America's political landscape in the 1988 election, when Lee Atwater managed the elder Bush's campaign and was able to link Michael Dukakis with Willie Horton via racist "soft on crime" campaign ads and Bush's continual harping on Dukakis as a liberal. Dukakis, foolishly, resisted the label, until a week before the election when it suddenly hit him that some of America's favorite presidents, like JFK and FDR, had been liberals.
Reagan, and by succession Bush Sr., did a lot to co-opt Christianity as a voting bloc, but I think the truth is that they were building on the powerful machinery established in Falwell's Moral Majority in the mid-1980s with its outrage over pornography, which most liberal groups defended as protected under the First Amendment; and then, of course, with the Summer of Mercy and the backlash against abortion.
The main problem with the Moral Majority was its view of morality as a series of rules that should be obeyed, and that should be established by society (via government, as society's erstwhile father), rather than as something that flows from a relationship. With the Democratic Party generally in favor of abortion as a woman's right to equality, and that platform creating a driving wedge between it and the evangelical/fundamentalist Christians who traditionally had been a reliable voting bloc on social issues, it only made sense for GOP strategists to manuever the party into the "values" camp -- something too many Christian leaders have been willing to go along with, to the point now that an entire generation of evangelicals has been raised with a politicized gospel, thinking too much on how the government can aid in fighting our social ills, and equating the faith with things like capitalism, democracy, trickle-down economics, and nonprogressive taxes.
And now look where we are.