Government neutrality is a central principle and touchstone mandate of non-establishment while church state separation is a method of achieving neutrality. Government neutrality both protects religion from state interference and provides equal protection before the law for those who dissent from religious orthodoxy. Separation can be, and often is, the only way, or at least the only practical way, to achieve genuine non-establihment neutrality. But no one method of achieving government neutrality is applicable or optimal in all contexts. Furthermore, the principle of a government obligation to be neutral also generalizes and abstracts to commercial and domestic partisan competition/activity.
Non-establishment is as much about protecting the civic status of minorities such as atheists and polytheists as it is about protecting religion from state interference. It is this minority rights aspect of non-establishment that is least respected and therefore most in need of advocates in the United States. When law and/or government practice favors one set of religious viewpoints it follows that the status of citizens whose viewpoints conflict or contradict the established religion is placed at risk of being diminished relative to their fellow citizens. Neutral government provides better protection for civil rights and is fairer. Freedom of conscience isn't denied by discrimination but discrimination also does harm and is thus objectionable. Establishment of religion is, by definition, discriminatory.