IIRC, a large segment of Fundamentalists/Evangelicals followed all along the philosophy of “in The World, but not Of The World” and were not politically activist, because the World was corrupt anyway.
Until the systematic organization of the “Religious Right” as a nationwide political lobby in the 1970s (Jerry Falwell, Ralph Reed, etc.), those of that description who could be rallied to political action were variously scattered all over the landscape, gravitating to whatever political machine or movement may jibe with their values in their particular location, and on their particular pet issue. Stands to logic, since traditionally Evangelical/Fundamentalist churches were quite decentralized – old-school Southern Baptists, for instance, would likely attach themselves to old-school Southern Democrats,* in their particular southern state*. Also, even among these, their primary concern was strictly conservative, that is, fighting a defensive action of their values against encroachment and erosion.
IMO the rise of the organized Religious Right in the 70s was rooted in a reaction to the (IMO exaggerated) perception that the left was running amok unopposed in the culture war (e.g. sexual revolution, hippies, anti-Vietnam-War movement, drug culture, social permissiveness, racial integration, urban unrest, decline of traditional religions) while America was becoming weakened abroad in the face of the godless commies(*). The paradigm shift that gave it life was to the effect that the penetration of the left into the system needed to be not just resisted, but actively rolled back and its effects undone, by working within the political system, in a concerted effort to “take back” society and bring it around to the True Way. It was the development of a nationwide-level convergence of groups that were conservative both in matters of faith AND of socioeconomic policy and willing to make something of it, while in earlier times they would have been fragmented among followers of one or another preacher or leader or of a regional-specific party machine.
(*)Sometimes they would sound like if only the Communists did not have an atheism plank in their platform and would allow freedom of religion, they would be willing to sit down and discuss politely the suppression of private property or proletarian dictatorship…
It may seem an oversimplification, but the national Democrat Party’s commitment to Roe v Wade and the Republican Party’s iffyness-turning-to-opposition to RvW became the galvinizing issue in the Religious Right’s hard Republican shift. While, IIRC correctly, Carter didn’t champion RvW, neither did he oppose it, Reagan actively lashed out against it. Incidentally, the abortion issue is one area in which Carter now does challenge the Democrat Party consensus- yay, Jimmy!
My understanding is that Carter does’t like abortions, really wants late term abortions to be for health/rape/incest reasons, but thinks Roe V. Wade should stand. I wasn’t aware that there was a true consensus in the Democratic party on exactly where to draw the line, but most Democrats I know take a similar stance to Carter’s.