[I]t shouldn't matter whether someone supports [laws banning -- or allowing -- abortion, infanticide, the destruction of embryos or chimpanzees for medical purposes, or the killing of members of endangered species might be sound or unsound] because of his belief that laws should turn on the greatest good for the greatest number, his belief that we are all sons and daughters of Gaea and must thus protect our environment, or his belief in the Bible. For most, quite possibly all, of us, our moral beliefs ultimately rest on unproven and unprovable moral axioms.
But Volokh is eliding a distinguishing feature of religious beliefs. It's not that they are merely unproven and unprovable. It's that they are claimed to emanate from an infallible, totalizing authority. Once you factor that in, it's not hard to see why religious reasons are peculiarly inimical to a secular, pluralist democracy.