I'm having trouble determining the best strategy in these kinds of games, but I'm worried it's not quite actually sounding like a member of the group you're pretending to be.

For example, a liberal Christian complained that her (honest!) Christian answer did very poorly, because people associated liberalism with atheism. This suggests that the best strategy isn't necessarily to honestly list what you believe, but to list what you think a typical member of the group involved believes.

And If (for example) atheists know that the average Christian is writing about what they think the average Christian believes, than atheists in their fake entries will also write about what they think the average Christian believes.

Yes, if overdone, this is a sign of dishonesty; for example, anyone who was too stereotypical ("Yeah, I get up each day, read a selection from the Bible, check the Pope's Twitter account, then go to church, then go bomb an abortion clinic..." would be obviously fake.) So the best strategy seems to write something kind of stereotypical, but to depart from stereotype in a few places so as to signal you're talking about a real person rather than a straw man.

But this strategy is identical for real Christians and sham Christians, which sort of defeats the purpose of the Ideological Turing Test. We're not testing whether atheists can talk like a real Christian any more as much as whether atheists can talk like a real Christian pretending to be a stereotypical Christian, which seems like a lower bar.

I'd be interested in seeing differences between this test and one in which, say, Christians were just asked to discuss their opinions on some topics without it being part of a Turing Test, and then atheists were asked to fake Christian opinions on those same topics (also interested in how those same just-discuss entries would do against Christians-writing-for-a-Turing-test entries).

Interestingly, the entry that I was most convinced was Christian - and I was right - was one that included the phrase "and when I was in seminary...". I didn't expect any atheist to have the chutzpah to fake a priest, whereas I did expect some actual priests to read Leah's blog. This suggests that a winning strategy is to be stereotypical in unexpected ways fakers wouldn't think of, and possibly to be unstereotypical in unexpected ways fakers wouldn't think of (although obviously I can't think of any examples of this).