Like it or not, serious rationality tends to erode religious belief, just as it tends to erode belief in astrology. It tends to erode blind obedience to other authorities too. If "word spreads and authorities find out", enthusiastic participation in any sort of rationalist community is liable to mean trouble in repressively religious communities, whether Eliezer is a raging bitter passionate atheist or not.

In any case, I'm having trouble imagining what the LW community could actually do to "try to distance ourselves from atheism and anti-religiousness as such" even if we wanted to, that would have any appreciable impact on the safety of being a serious rationalist in the sorts of countries you're talking about. Go back through the LW archives and delete every post that says unkind things about religion? Forbid discussion of religious topics? It seems absurd to respond to the threat of oppression by meekly oppressing ourselves; and besides, I bet it wouldn't work. There's too much other stuff on LW that would be offensive to those regimes.

What it comes down to is this: A rationalist in a sufficiently repressive irrationalist regime is going to have to pretend not to be a rationalist. That's very bad, but having rationalists everywhere else pretend half-heartedly not to be rationalists about everything won't solve the problem.