To me the question is whether the mainstream American Left or the mainstream American Right is more authoritarian. You can't look at extremists on either side because extremists are almost always going to be authoritarian regardless of their ideology. So really its a question of what does the Democratic voting base support vs what the Republican voting base supports.
The Democratic base tends to support social liberalism, is pro-choice, is pro-drug decriminalization, is pro-gay marriage, is in favor of strong environmental protections, is in favor of universal healthcare, in favor of reductions in defense spending, and in favor of progressive taxation.
The Republican base tends to be socially conservative, pro-life, anti-gay marriage, in favor of strong defense spending, in favor of less regulation, and in favor of a flatter tax system.
If we look at authoritarian requiems throughout history we don't see too many of them that arise due to progressive taxation, reductions in defense spending, strong environmental regulations, universal healthcare, or social liberalism. In fact, I can't think of a single authoritarian requiem in all of history that came about in that way. Usually authoritarian regimes come about either by social conservatism and the mixing of church and state or by a government military industrial complex that convinces its citizenry to give up freedoms in exchange for security. So while you could argue that the American right is in favor of more economic freedom than the American left, the authoritarian problem on the American right is their embrace of militarization and their rampant social conservationism - which is inherently authoritarian. Using the state as a vehicle to endorse, promote, or compel your cultural and or religious moral views is by definition authoritarian. Drug laws, anti-sodomy laws, blue laws, mandatory sentencing, dry counties, book bans, and all sorts of mixing of church and state have all been brought to you by the American Right, so I don't think they have a leg to stand on when accusing the left of authoritarianism.