Some dogma cannot be rejected.  Those dealing with the fact of the Resurrection and the shared beliefs on the Trinity are non-negotiable.  Moral law, however, is not a matter of conscience as much as a matter of human nature, which is knowable by both reason and evidence.  If the evidence for ignoring doctrine is profound, than it is a violation of conscience to not speak up.  The same is true when the Church acts corruptly, like in its support of the American pro-life movement, which is essentially a Republican confidence game.