I finished the Strauss book I'd been reading. I'm still not sure what his deal is. Perhaps his esoteric doctrine is just too well hidden, but as I understand his esoteric/exoteric distinction, there's supposed to be an obvious exoteric doctrine; I didn't see one of those, either.
It is possible that I have difficulty understanding him because his Judaism was too important to him, and that's just something I don't get. He seems to have been an atheist, but atheists seem to differ depending on their backgrounds. Judaism, and to a slightly lesser extent Catholicism, are just deeper than Protestantism, so atheists from those backgrounds often still show strong connections to the traditions that they were raised in.
One thing I am sure of is that Strauss totally misunderstands Nietzsche on religion, and that's one of the reasons I wonder if this different kinds of atheists issue is at work. Nietzsche was a Protestant atheist (like me). He was interested in Christianity and Judaism since they were vastly important historical phenomena, but their personal significance for him was not actually all that great (he speaks of his atheism as an "instinct"; atheism is not instinctive for anyone who remains strongly connected to any religious tradition). Thus, I think Strauss is totally off-base when he attributes covert religious doctrines to Nietzsche; Nietzsche's philosophers of the future were certainly to do without worship of any gods (though perhaps not without ass festivals).