You've thrown out "effort to prevent people from saying that which is undesirable" as an example of Democratic authoritarianism. However, this is not a mainstream grassroots view. Rather it's the status quo agglomeration of power by politicians, the government grabbing power while entrenching the big tech oligopoly. Democratic voters in general don't seem to be sitting around going "Biden is going to shut those deplorables up", rather it's more like lament and resignation when the topic of social media censorship does come up.

We can of course point to authoritarian policies enacted by politicians from both parties, because politicians are inherently authoritarian, and enacting authoritarian policies that enrich their sponsors is their bread and butter.

However, the cults of personalities around Republican politicians, the rejection of intellectualism, overtly excepting politicians from the rule of law. These all indicate an authoritarian-flavored organizational structure, supported by the grassroots. If fronting as a strongman and pulling stupid stunts didn't work to get votes and donations, Republican politicians wouldn't do it. And the recent state level pushes to prohibit fundamental medical care (ie straight up individual liberty-destroying dark ages authoritarianism) is policy that doesn't enrich any corporate sponsors (as legislation usually must), but rather seems to be completely at the behest of their perceived constituents.

And so, I no longer consider the two parties symmetric. The Republicans have seemingly made their mainstream platform to dismantle our institutions in favor of regressing to some sort of good-old-days theocracy, while the Democrats still basically represent the corporate/bureaucratic status quo. And while I find that status quo repugnant from a position of wanting to reform it in favor of individual liberty, I'd much rather have the imperfect institutions we've come to take for granted, like the rule of law, than have them destroyed from the top down.