This looks like an interesting study discussed in Roll Call (subscription required). The link between Congressional voting and religion may be a bit more tenuous that seems to be suggested. I am not sure the link between regligion and party ID is not stronger than the researchers may believe, but at least someone is looking at the issue.
It has been widely known that churchgoers vote in elections far more regularly than non-churchgoers. But whethe Congressmen allow their religious beliefs to influence their voting patterns is not as well known. I would imagine that on inherenly moral issues (such as abortion or right to die matters) that there may some correlation between religion and votes, but whether religion influences the more day to day voting patterns seems a little far-fetched to me. So much of Congressional voting patterns can be traced to partisan identification and consitutent needs/desires.
I hope to be able to get this study sometime soon.
For First Time, Scholars Link Voting, Religion