The individual states that are responding the best are all heavily liberal/democratic led states - CA, WA, NY, IL. Some of the less liberal states are doing good (OH), but most are doing really terribly (FL). The evidence seems to point in the direction of working democratic government being best suited for handling this crisis. Since the world largely does not have working democratic government in 2020, we have a pandemic.
I have so far seen zero reason to believe that if the outbreak originated in Kansas, or Poland, or Bangalore, it would not have spread across the world by now.
The difference in reaction between red/blue states has less to do with liberalism/authoritarianism, and more to do with the anti-science bent of the modern US right.
devils advocate, but if it ends up that democratic states don't handle the response as well as authoritarian ones out of differing views of individual rights, this isn't necessarily a 'win' for the democratic side of the fence