Gallup has released an analysis of how support for various presidential candidates breaks down by church attendance. Somewhat surprisingly, in a general election match up, Hillary and Rudy are neck and neck among non-church going whites.
Most of this aggregate split is attributable to the ambivalence of non-church going independents. Here's what Gallup reports:
Overall, 54% of whites say they would vote for Giuliani if the election was being held today, while 41% would vote for Clinton. This is testimony in and of itself to the dependence Democrats have on ethnic, non-white voters to win elections. But white voters are by no means monolithic in their support for Giuliani. White frequent churchgoers are particularly likely to support Giuliani over Clinton. Six in 10 whites who attend church at least monthly pick Giuliani, while only about one-third pick Clinton. But among that group of whites who seldom or never attend church, it's a different story. Clinton has a slight 3-point advantage over Giuliani among whites who seldom or never go to church, 49% to 46%. This relationship between religion and choice of candidate occurs for the most part among whites who classify themselves as independents -- who are by definition less likely to be firmly attached to one party or the other's candidate. Among voters who identify as Republicans or Democrats, however, there is substantial party loyalty; the strong majority of both white Republicans and white Democrats -- regardless of how frequently they attend church services -- say they would vote for their party's candidate.