"President Reagan leveraged the Southern Evangelicals for his political needs"
Liberal and conservative elements existed in both parties until LBJ, and Nixon, both more liberal leaning. FDR and Hoover, if you recall, really advocated the same policies. FDR just continued what he started. Christians didn't have a specific party. Religious people tend to be more conservative anyway, but with most of the population identifying as Christian at the time, there really wasn't space for a party-religion association.
What I think Reagan did was polarize an already strong conservative base into the one party using both the economy and the newly hot-button issue of abortion. As an incredibly good speaker with a disarming personality. He pulled a lot of people onto his side, but he would never have been successful if the social mood, so to speak, was not already largely in his favor.