My initial argument was about how infection rate is not strongly correlated to policy.
But to assume that, you also have to assume Democratic areas don't have different policies, negating the entire premise of Democrats being more restrictive than Republicans.
The only reason it's hard to point to policies having an impact is that it's very hard to measure policies on any kind of uniform scale when they vary so much from jurisdiction to jurisdiction. Even after you somehow rate policies, you're left with unequal enforcement. Political leaning is an objective and binary piece of cake.
If you take for a given that Democrats imposed more restrictions, knowing Democrats fared better proves restrictions helped or at the very least didn't hurt.