My hypothesis is that LW is actually not politically neutral, but some political opinion P is implicitly present here as a bias. Opinions which are rational and compatible with P, can be expressed freely. Opinions which are irrational and incompatible with P, can be used as examples of irrationality (religion being the best example).

Yeah, that sounds about right.

Opinions which are rational but incompatible with P, are self-censored.

Not entirely, but I agree that they are likely far more often self-censored than those compatible with P. They are less often self-censored, I suspect, than on other sites with a similar political bias.

Opinions which are irrational but compatible with P are also never mentioned (because we are rational enough to recognize they can't be defended)

I'm skeptical of this claim, but would agree that they are far less often mentioned here than on other sites with a similar political demographic.