I don't know what the author of the song "Church of Logic Sin and Love" (by The Men) meant by it. I've just borrowed the three words, since they serve as central figures around which I can discuss what I think religion is about.
Love: There won't be much if anything on this topic, not because it isn't supremely important -- just that I have nothing new or unusual to say about it.
Sin: In my view, religion isn't religion unless it acknowledges Original Sin, or something similar. In Hinduism there is Maya, in Buddhism, Ignorance. Granted, I don't think the Christian tradition of Original Sin as being "disobedience" plays well any more, nevertheless, I accept the notion that there is something fundamentally wrong with us, and it has to do with being out of touch with the transcendent. They are most out of touch who deny the reality of the transcendent.
Logic: In this blog, the word "logic" should be treated as the adjectival form of the word "Logos", as in: By [the Logos] was everything made that was made. Logic, then, becomes a means to Logos. The usual meaning of the term, which I shall identify as Aristotelian logic, is what you get when you restrict one's thinking to the sense perceptible (the spatiotemporal). It is of little value when directed at the mental, or the transcendent. But (see Sin), attempts at creating a logic that is of value in these areas is fraught with peril. Which is why the apophatic tradition exists. I think, though, that something can be done that is more positive.