Evangelicals were not a special interest group. You see them that way now, but they were (and are) normal people in the 1960s and 1970s who became organized around principles they saw the Republican Party drifting away from, right or wrong. Reagan’s governorship and the loss of seats by moderate Republicans in the California legislature were their first early victories. They did this a step at a time, in states throughout the country, imperfectly at times. Unlike the Left, they didn’t take their toys and leave when they experienced losses.
I think it’s you and others on this board that need to read history. The Democratic Party didn’t become the party of civil rights overnight—it changed. The Republican Party didn’t eschew progressivism overnight in the early twentieth century—it changed.