Step by step.

I read a really good history of the Southern Baptist Convention, a couple of years ago (sadly, I forget both author and title) that documented the conscious decision by which the national leadership of the SBC, during the Reconstruction, made a conscious decision to be the voice of moral authority on the Confederate revisionist side, to embrace and defend the religious and social complaints of the former slave-holding class in the old Confederacy. So by the time of the rise of the Religious Right as we know it, the Southern Baptist Church had already invested nearly 100 years in raising, training, and providing volunteers for pro-segregation candidates in both political parties. After Democratic President Lyndon Johnson signed the Civil Rights Act, that put the Southern Baptist Church firmly on the Republican side.

Also in 1964, at the presidential nominating convention (per the speeches and writings of Goldwater delegate and best-sellling conspiracy theory author John Stormer), was the meeting of the Republican Anti-Communist Caucus at which the leader of the top fundamentalist seminary in America, Dallas Theological Seminary, committed to revising the curriculum to persuade all future fundamentalist ministers that fighting Communism was Christian cause number one, and to teach that it was therefore a religious duty of all Christians to support politicians from what they saw as the only reliable anti-socialist, anti-communist party, the Republicans.

In 1968, the Pope of the Catholic Church issued the encyclical Humanae Vitae, which, among other things, banned the practice of contraception or abortion. By 1968, feminism was already seen as a left-wing political cause for long enough that it was being paid lip-service by even center-left politicians in the Democratic Party, which fairly rapidly coalesced into the current situation where observant Catholics feel forced into supporting the only anti-feminist political party, the Republicans.

In the second volume of his auto-biography, Francis Schaeffer, Jr., the son of the famous evangelist (and founder of the modern fundamentalist movement) Francis Schaeffer, documents that it was his personal revulsion to the idea of legal abortion, after 1973 Roe v Wade, that persuaded him to argue his father into telling wealthy Protestant fundamentalists that opposition to abortion was the most important Christian cause, and that they needed to donate money that funded the founding of Moral Majority. Schaeffer Junior says that he approached politicians in both parties, offering them the support of Moral Majority if they would denounce legal abortion, making the argument to Democrats that the traditional Catholic origins of organized labor and their traditional embrace of government regulation made anti-abortion a Democratic cause, only to find himself out-maneuvered by feminists on the platform committees and organizing committees. So, he says, he had no choice but, as their lead fund-raiser, to encourage early Moral Majority leaders to embrace Republicans, and their embrace of traditional rural values (see neo-Confederacy, above), as the only hope of seeing legal abortion overturned. (A decision he now says he regrets, but feels that the feminists left him with no alternative.)

tl;dr: Post-1964, the Southern Baptist Church embraced the Republican Party for segregationist reasons; post-1973, Moral Majority and the Catholic bishops both embraced the Republican Party for anti-feminism reasons.

I did some writing on this topic 25+ years ago, and while I've since moved in entirely different directions I still have some of the resources on my shelves. For those interested in authors trying to make sense of this linkage soon after it happened (primarily 1980s) I'd recommend the following books:

• Baker, Todd A. et al., "Party Activists and the New Religious Right," in Charles Dunn, (ed.)Religion in American Politics. Washington: CQ Press, 1989

• Capps, Walter H. The New Religious Right: Piety, Patriotism, and Politics. Columbia: University of South Carolina Press, 1990.

• Conway, Flo and Jim Siegelman The Holy Terror. New York: Doubleday, 1982.

• Guth, James L. and John C. Green (eds.) The Bible and the Ballot Box: Religion and Politics in the 1988 Election. Boulder: Westview Press, 1991.

• Hadden, Jeffrey K. "Conservative Christians, Televangelism, and Politics: Taking Stock a Decade After the Founding of the Moral Majority" in Robbins, Tom and Dick Anthony (eds.) In Gods We Trust:New Patterns of Religious Pluralism in America. New Brunswick: Transaction Publishers, 1990

• Hertzke, Allen D. Representing God in Washington: The Role of Religious Lobbies in the American Polity. Knoxville:Universtity of Tennessee Press, 1988.

• Hill, Samuel S. The New Religious/Political Right in America. Nashville: Abingdon Press, 1982.

• Jorstad, Erling The New Christian Right, 1981-1988. Lewiston: Edwin Mellon Press, 1987.

• Leibman, Robert C. and Robert Wuthnow (eds.) The New Christian Right: Mobilization and Legimation. New York: Aldine Publishing Company, 1983.

• Pierad, Richard "Religion and the New Right" in Wood, James E., Jr. (ed.) Religion and Politics. Waco: J.M. Dawson Institute of Church-State Studies, 1983, pg.60-ff.

• Shupe, Anson D. Born Again Politics and the Moral Majority. Lewiston: Edwin Mellon Press, 1982.

• Viguerie, Richard The New Right: We're Ready to Lead. Falls Church: The Viguerie Company, 1980.

• Wilcox, William Clyde God's Warriors: The Christian Right in 20th Century America. Baltimore: Johns Hopkins University Press, 1992.

One thing that hasn't yet (as of this posting) been raised is the practical link between the GOP and the religious right in the 1980 campaign. The GOP needed to reach socially conservative voters, including those who might have soured on the party in the post-Nixon era and been otherwise nonplussed by Ford. Several organizations within the political and religious rights, most obviously the Moral Majority but perhaps more importantly Richard Viguerie's Conservative Digest cronies, had developed direct mail operations (and thus had mailing lists) that were more extensive than the GOPs. They ultimately agreed to support Reagan, share their mailing lists and technology, in exchange for a slate of promises on socially conservative issues (school prayer, abortion, anti-communism, etc.) that Reagan's campaign was happy to accept. Though Reagan carried the label "conservative" happily and was a pro-forma believer, neither he nor his advisors were actually supporters of the religious right's core agenda-- they just used them effectively as allies to GOTV and counter-attack their Democratic opponents on cultural issues.

I would say that the presidential election 1980 (Carter vs. Reagan) pretty much sealed it. Even though Carter had made headlines for being born again, and Reagan was anything but evangelical, he was the first Republican to capture the heart of the evangelical movement with his conservative, success-oriented, red white and blue rhetoric.

I grew up in the evangelical church. The 1980 election is the first time I remember church being so political. We were afraid in those days, because of the Iran-hostage crisis and the rising price of oil and the growing threat of Communism. In 1979/1980 there was a decided shift in the direction of Christian preaching and publishing, from "Let's tell the world about Jesus" to "Let's work together for a strong America."

Since then, evangelicals have vacillated between the idea that America is the New Babylon (when there is a Democrat in office) or that America is the New Jerusalem (when there is a Republican in office).

A lot of good things here—I'm just going to add a regional perspective and suggested readings. Evangelicalism and the New Right (as this version of Republicanism is often called) became linked the strongest in the South and the West. In the South, as mentioned elsewhere, race and civil rights were defining and complex issues. For how conservative religion gets in to this mix, see Miller's Billy Graham and the Rise of the Republican South. In the West, it played out a little differently, often with white suburban professionals (especially transplants from the plains) found community ties in churches during a transitional political period. See McGirr's Suburban Warriors: The Origins of the New American Right, especially chapter 6.

No one else has mentioned it. "Don't Think of an Elephant" by George Lakoff talked greatly about how James Dobson and Focus on the Family moved Evangelical Christianity into a wealth=moral fortitude type of mentality. The idea that God only allows the people who are upright Christians to be successful and wealthy is one they capitalized upon and were able to use that value-speak to cause a lot of people who often voted with the Democrats (particularly the blue-collar labor class in the South and Midwest) to side with the Republicans.