It's pretty clear cut to me. I can't envision a world in which Democrats were less authoritarian on COVID. For one simple reason: Democrats align themselves more with academia while Republicans align themselves more with small business. Small business more than anyone had the incentive to stop the lockdowns, whereas the medical establishment had multiple layers of incentives (including from Fauci's personal entanglements) to perpetuate the Covid myth.

As for Republicans being bad on Covid at first, everyone was pretty much on board with the authoritarianism at first, because we weren't sure what we were dealing with. "Two weeks to stop the spread," is what we were sold and most people were willing to put up with that.

But two weeks turned into years; even as data was coming out that Covid wasn't dangerous except maybe for the elderly. Moreover, the George Floyd protests showed that 1) Covid wasn't that dangerous; 2) lockdowns were being selectively enforced.

I'm not saying Republicans aren't also authoritarians. I just think that on Covid, specifically, it was pretty clear cut to me the differences between the parties. And since Covid brought about the most egregious violations of liberty we've seen since 9/11, it makes sense that libertarian leaning people harbor distrust towards Democrats.