They depend on their leaders to tell them what they believe. It's the same on the national level. There are a few, well-known, celebrity pastors, mostly of the megachurch, television preacher variety, who have an inordinate amount of influence because of who they are, far greater than just the reach of their congregation.
The big names back in the late 70's when they first decided to put their support behind a GOP candidate, picking the divorced Reagan as the guy they were going to support, a man who couldn't remember the last time he'd been in church, who had been divorced and remarried, a no-no for leaders in conservative churches, and who had no clue about their doctrinal beliefs, were Jerry Falwell, Pat Robertson, and a Texas evangelist, James Robison, who was a pulpit screamer. There were also people behind the scenes pulling strings, but not wanting to dirty their own reputation by getting involved in partisan politics. That would be Billy Graham. He was a major influence in the "Religious Roundtable" via Ed McAleer, but wanted to protect his ministry and reputation from the fallout that would come if people knew.
They've succeeded in making points from right wing extremist politics doctrinal beliefs of the church, so people think those points are part of the Christian gospel, when they're not. And yet, when you challenge an Evangelical to justify their support for politicians whose morals are diametrically the opposite of Christian teaching, their response is some trite saying like, "I'm not voting for a pastor in chief, I'm voting for a commander in chief." Or, "God used King David and he wasn't perfect." Both of those statements are contrary to any Christian teaching, and gross misuse of the Bible.