This makes it seem that red states are being hit hardest on this which doesn’t seem like that should play as large of a role in gas prices as, say, infrastructure.
Am I seeing a false pattern? Or is there a set of policy measures that blue states have implemented that red states haven’t to prevent gas price spikes?

I don’t think that’s it.
Don’t want to share anything identifiable, but I get semi-regular updates on things in 3 parts of the US. So anecdotally speaking, the chart lines up almost perfectly with what I’m seeing across those areas. Before the war, there was maybe a 5-10% (~$2.50 in Republican vs $2.75 in Democrat) spread in gas costs, but now its almost 30% spread (~$4.25 in republican vs $3.25 in democrat).