According to Rawlsians, it is wrong to make decisions in the public arena based on controversial comprehensive doctrines.
Here is a counterexample. We meet up with aliens who are incredibly truthful: not only have we never found one to lie, but we have never found one to even accidentally say the false. The aliens inform us that they have figured out whether controversial comprehensive doctrine D is true. We have very good reason to believe the aliens. The aliens inform us of a fanatical plan: Each state has two weeks to submit a statement to the aliens as to whether D is true. Those states that either fail to submit such a statement or who get the answer wrong will be completely destroyed. And then the aliens will leave.
It is obvious that the right thing for the state to do is to do its best to figure out whether D is true, and then on the basis of its best determination make the statement to the aliens. It is clearly wrong to refuse to answer, and it is also clearly wrong to simply guess without basing oneself on one’s best determination of the truth value of the comprehensive doctrine. It is clearly the right thing in this case to make a public decision on the basis of a controversial comprehensive doctrine.
Of course, this is a very special case: a case where what rides on the decision is so important that it trumps most other considerations. But we can lower the amount that rides on the decision and still keep the intuition. Suppose that instead the aliens promise to kill one per thousand people at random if we get the answer wrong. That should, I think, be enough to overcome any qualms we may have about using controversial comprehensive doctrines in public policy. But now there are real-world issues riding on controversial comprehensive doctrines where what is at stake is of a similar or greater magnitude. Abortion is a paradigm case.