Religious Left
No, it's an assumption that Democrats are less likely than Republicans to use churches as a way of organizing politically.
Tell that to Jesse Jackson, Al Sharpton, and a few others. ;)
The religion of the far Left, insofar as "religion" might be defined as beliefs firmly and fiercely held in the face of all opposition and despite a serious lack of objective evidence, is probably collectivism and its subset of socialism.
If you substitute the State for the deity of your choice, the religious nature of a lot of Democrats becomes fairly clear. The State is the source of all good things. I could have some fun working this analogy into the ground...
And believe me, I've seen leftist rallies that would match any revival meeting.