How would a "religious left" feel about abortion? I would likely see them still being pro-life (like "Pope Francis Catholics" or liberal Mormons) which could cause conflict with the Democrat leadership
I imagine the religious left would be more focused on economic issues than social issues. Currently, the religious right is focused on their religious social issues (social conservatism) while totally ignoring their religious economic issues (programs for the poor, etc), so I don't think it's too much of a stretch to say certain religious people could ignore their party's social leanings if they side with one another in economics.