That's adorably simplistic. Your clear bias aside, oil and gasoline prices are not tethered to one another. Gas (a refined product) pricing is only impacted by supply and demand in the most extreme circumstances (like pandemic). There are many other forces at play in that industry. Why does fuel get cheaper in election years? Demand doesn't change but prices do. Tons of books (its like Facebook but on paper and without click bait) to learn about elasticity and inelasticity. It's fun to throw opinion stones and takes just so much work to learn and be educated.
In regards to political party influence, I'd imagine your referencing fuel taxes and yes tend to be higher in states that use those taxes to fund infrastructure projects. It's the yin and yang.
Now show me on the stuffed bear, where the mean Democrats hurt you