Required reading for any discussion of religion and democracy:
“No ethical community could sustain a discursive practice without imposing on each of its members the necessity of keeping track of the normative attitudes and entitlements of their interlocutors, because without this there would be no communication—and therefore no exchange of reasons—among them. But, as we have seen, ethical communities have different ways of going about their discursive business. […] Where the default position in a given community is that the ethical judgments of those in ecclesial or political office are correct, we have a pattern of deference to one kind of authority. The authoritarian extreme is reached whenever such a position is treated as indefeasible and the authority is treated as self-interpreting. As one approaches this extreme, ethical truth is reduced in practice to what the highest authority says. When the reduction is total, it no longer makes sense to claim that the highest authority says P, but P might not be true.
“One should not assume, however, that all religious communities are huddled near the authoritarian extreme of the spectrum. Many religious traditions and movements have developed relatively flexible structures of authority, and even those best known for their official rigidity are rarely able in practice to stamp out critical questioning of allegedly indefeasible authorities. […] Many Protestants, Jews, and Muslims who begin by attributing indefeasible and unique authority to a revealed law end up interpreting that law in a highly flexible way. All of these traditions have been more pluralistic and less authoritarian in practice than some of their officials and intellectuals have wanted them to be.”
-Jeffrey Stout. Democracy and Tradition. Princeton, New Jersey: Princeton UP, 2004. (280)
I ellipse'd out his brief discussion of the Roman Catholic church. Of course, “papal infallability” is one of the rare explicit cases in Christianity where a religious authority literally maintains that if the highest human authority “says” P, then it cannot be the case that P is false. But I've learned that what it means for the Pope to invoke the doctrine is kind of complicated. Furthermore, infallability is only invoked rarely. And I'm a Presbyterian, so I'm under no obligation to defend it Roman Catholic doctrine. So I think we can skip the RC wrinkles for now.
Now, I believe most Christians would hold that if God says P, then we shouldn't suspect that P is false. But we can always suspect that we didn't understand what God was saying. Interpretation is difficult. (But nothing worth doing is easy.)
I'm trying to imagine how you could plausibly level a charge of authoritarianism towards Presbyterians. We've got a General Assembly, so issues are decided by committees, representatives, and votes. Perhaps a current general assembly could start acting unilaterally—but it would only be a matter of time before their replacements arrived.
The same thing is true for denominations with stronger ecclesiologies. The turnaround just takes longer. The channels for change aren't as speedy (on paper, at least) as those of a democracy, but they exist. This keeps most religious traditions of any size from approaching the authoritarian extreme. A group that closes off these channels will eventually find itself an isolated sect, or even a cult.
To be authoritarian in Stout's sense requires the necessary force to stamp out opposition. And whatever power the Religious Right has in the United States, it doesn't have that. It's far from having it. And I suspect that almost nobody wants them to have it.