Second, if you are arguing for some kind of turn towards the religious communities, it seems to me you have some responsibility to explain what it broadly requires without sidestepping this as "nuts and bolts questions of practical organizing, which can ...be only discussed productively in the context of actual organizing."
Are you proposing that list members join their local church, mosque, or synagogue? Many are non-believers who would balk at participating in the religious rituals and agreeing with the substantial body of doctrine which would be expected of them as a condition of being accepted. If they passed these barriers, I don't doubt that there would be more and better possibilities to intervene in the internal life of these institutions in the same way as direct participation in a working-class party or union is always more rewarding than standing outside of them. But what evidence is there that receptivity to left-wing ideas in religious organizations would be greater than in the traditional venues where working people discuss social and political questions and issues directly affecting their living standards?
If, on the other hand, you are simply trying to underscore that the left has to better identify, be more understanding of, and seek ways to collaborate with progressive groups and individuals within the churches, that's hardly controversial. I'd say the same about the left's orientation to the Democratic party, the other big influence on liberal wage- and salary-earners in the US. But I think you want to see more than this, without spelling out what it is that you want.