The short answer is: maybe not. In recent elections, during the period from 1992-2004, turnout among Evangelical Christians increased. Conventional explanations emphasize campaign strategy, especially those that investigated the Bush campaigns of 2000 and 2004. For example:
bq. Mr. Rove’s relentless focus on turning out more Republican voters, many of them evangelical Christians, was the critical factor in Mr. Bush’s victory, Republicans said.
In fact, there is new evidence that the mobilization of Evangelicals may have had more to do with demographics than campaign strategy. This is the conclusion of a newly published paper by Ryan Claassen and Andrew Povtak. They write:
bq. We find that, contrary to conventional wisdom, the increase in Evangelical turnout appears to have been driven by social and demographic changes among Evangelicals rather than by a political strategy. In fact, controlling for social and demographic changes, we find more impressive turnout gains among other groups, such as black Protestants and the nonreligious.
bq. In light of changes among Evangelicals that have made them more prosperous and better educated as a group, one would expect increased participation even in the absence of moral issues on the national agenda, born again candidates, and voter guides.
Moreover, it appears that an equally, if not more important story, involves increases in turnout among black Protestants and the non-religious:
bq. …increased turnout among secular voters and black Protestants has received far less attention recently (no doubt because the Democratic party did not emerge the victor in the 2000 and 2004 presidential elections), the raw increases in turnout over time are even more impressive than those of Evangelicals and they appear to be less a function of sociodemographic changes in the groups.
The main caveat is that this account focuses only on turnout, not on the changing partisan loyalties of Evangelicals. Nevertheless, I think this piece poses a significant challenge to conventional wisdom.