Rather, cars are almost always more convenient, more comfortable, and faster than public transportation, the sole exception being the central cores of large cities. So people outside said central cores will always choose them, given a chance.
But cars are also much more expensive than public transport or bicycle. So they are driven more by richer people, who tend to be more right-wing. Poor people often move to central cores because they cannot afford to own a car, hence urban areas tend to be more left-wing than rural or suburban areas.
Correlation is not causation.
Public transport pays a bigger share of its infrastructure and has a lot fewer externalities.
Let's get the full price in (tolls for road use, emissions taxes, and full insurance payments for all healthcare associated at least with car accidents) and let's see what happens then. In the long run, we're all dead. John Maynard Keynes
One problem with arbitrarily raising the gas tax in a country like the US, with minimal public transport and low minimum wages, is that it would be very regressive, and might actually drive poor people out of the labor market. Some kind of rebate would be necessary.