With the invaluable help of special Tarkovsky correspondent Diane, I've managed to puzzle out some of what I found confounding about The Sacrifice. As better film thinkers than myself have long ago discovered, The Sacrifice is a syncretic story; it melds elements of Christianity and pagan thought, to jarring but intriguing effect. Apparently Tarkovsky had intended (in a different film) to tell a story about a man who goes to a witch for some healing (which would turn out to be sexual healing). Tarkovsky didn't get that essentially pagan story told as originally planned, so later he just kneaded that story into the otherwise Christian film Sacrifice. Which is really jarring if you're trying to put the movie into a rigourously orthodox Christian framework!
This kind of sycretic stuff is of particular interest to me right now because I'm reading Mallory's Le Morte D'Arthur. It blends overtly Christian stories and themes with various pagan tales, to confusing effect. Chivalric love between knights and married women is glorified and romanticized, until suddenly the story switches gears to the quest for the Sangraal, and formerly awesome knights like Lancelot find themselves dropping all the balls because they're only good at worldly valour; their adulterous sin-sickness makes them worthless for Grail-Questing. Which sounds pretty logical summarized like that, but in the text it seems that the author wholeheartedly approves of Lancelot and Guenevere's love. Then suddenly he doesn't. That's what happens when one editor tries to patch different tales from different authors into one overarching continuity.
Getting back to the Sacrifice, I suspect that one reason Tarkovsky chose to have God's will work through adultery is that it serves as an objective correlative of the many ways God in the Scriptures surprises His own followers and violates their expectations. It's a recurring motif throughout the Bible; God makes demands on people which they find incomprehensible. And in The Sacrifice, God makes a demand which seems to violate any reasonable expectation for the Christian God's methodology. I don't think Tarkovsky would ever expect God to work this way either, but he would expect God to work in mysterious ways, and this narrative choice communicates that quite effectively.
I have many more thoughts about this film; for all the fine movies I've seen since joining Netflix, none has gotten me puzzling so much. I'd better get to work, though.