As GP said in another reply, the incumbent party won a landslide victory in recent congressional election (180 out of 300 seats), so it seems South Koreans generally approve how the government handled it. (Of course the timing was fortuitous for Moon: had the election happened ~45 days ago things would have been very different.)
Even for the opponents, it seems the majority criticism was that the government didn't do enough - somehow they're very angry about not blocking visitors from China. (Many conservatives have a strong pro-America, anti-China sentiment, and frequently accuse the president of being the opposite.)
You don't have to be a conservative to see how the gov't screwed up early on -- the SK gov't went against the advice of the Korean Medical Association to restrict travel from China; instead the current Moon administration made a political decision to keep their door open to China to please Xi JinPing of China. The problem for the minority party was their link to Shincheonji, a cult responsible for the majority of all coronavirus cases, and they really had to keep their head down pretty much throughout the whole ordeal.
I consider myself a newbie and neutral on SK politics and had dismissed all the criticism of Moon being a commie and all before, but I'm starting to see through the garbage now.
Well, AFAIK, expert opinions were divided: many doctors were against border closing, saying that it will cause more people to enter illegally and hide, and then we'll have a harder time tracking them. (It's just a short boat ride across the Yellow Sea from China: you can't block the entire coastline.)
We may argue which side was right in retrospect, but it's not like Moon ignored the expert consensus.
Besides, Korean Medical Association is not exactly a neutral expert organization. The current head of KMA is this guy here [1], with pickets reading "Impeachment is void! Stop framing innocent President Park! Let's rescue innocent President Park with people's power and restore her honor!" blah blah, referring to Park Geun-Hye, kicked out in 2017 after corruption scandal.
Even for the opponents, it seems the majority criticism was that the government didn't do enough - somehow they're very angry about not blocking visitors from China. (Many conservatives have a strong pro-America, anti-China sentiment, and frequently accuse the president of being the opposite.)