As fundamentalists becoming evangelicals we got involved in politics because of fear stories.
At its heart each story was about losing rights we thought we were guaranteed as Americans under the Constitution: freedom of religion, conscience, assembly, etc. The details varied by issue and story: tax exempt status, government oversight of church organizations and functions, school prayer, religious expression at public occasions, etc. They took place against a background of Cold War church persecution stories, particularly behind the Iron Curtain. We told ourselves these stories for several reasons, including to cultivate a feeling of kinship with the modern persecuted Church, but they tended to galvanize our sense of ourselves as American Christians (or “Eisenhower Christians”), blending our two identities and seeing an assault on one as an assault on the other. We had in a sense participated in the Cold War ideologically, taking our stand against godless Communism, and and somewhere along the line got our American identity mixed up with our sense of ourselves as Christians.
In retrospect a lot of our sense of kinship with the Cold-War-era persecuted Church was pretty shallow; it had a lot to do with reading books about real bravery in the face of persecution (Brother Andrew) and fictional portrayals of persecuted Christians. In my case in particular, Myrna Grant novels about young believers in the Ukrainian underground church helped reinforce the impression that the Cold War was primarily a struggle for religious freedom.
As a result, though, we chose our political affiliation because we were afraid of the ACLU, because they sued to stop school prayer, and certain elements of the federal government because of the ongoing case against Bob Jones University, not for preaching the Gospel, but for violations of civil rights. There were at least a handful of other cases as well, including the case against Lester Roloff, where we saw religious persecution but the legal question was more about government oversight of non-religious functions of religious institutions: health and safety, corporal punishment, fire codes, etc.
But I think I would argue that what had happened was that we had hyphenated our Christianity and our nationality, and we got involved in politics not because of doctrinal or moral issues, but because we believed our rights as Americans had been violated.
The other issues that became hot-button issues: the Equal Rights Amendment, abortion, political correctness, gay rights, etc. were initially other people’s issues, and we adopted them as we got more involved politically. They were part of the process of becoming the Religious Right, and making common cause with people we suspected were going to Hell: Roman Catholics and mainline Protestants first, then later Jews and Mormons. Our political handlers sold us on the importance of these issues as they tried with mixed success to turn us into a coalition.