I've become hyper-aware of the 'both sides' that's been going on for some time, so this stood out. No, both sides did not do this. Democrats followed the science as it was at the time, following the advice of the virologists. It was the Trump Rightwing and so-called "conservatives" who decided to ignore the medical field, find their own quacks, and promote the opposite of whatever the Democrats proposed.
That's playing politics with public health and peoples' lives.