To complement other answers without directly invoking Newton’s law, the asymmetry comes from energy.
The asymmetry between car and Earth comes from the fact that car has to consume and spend energy (do work) in order to change its position.
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Actually we can even forget about energy and go further by saying that car transfers its momentum to earth. Imagine an asteroid flying towards us with constant speed: it is totally equivalent to Earth flying towards an asteroid up until the moment of collision or in other words both reference frames are inertial/immutable until they interact.
According to momentum conservation: while distance between Earth and asteroid changes simultaneously for both objects (so it doesn’t matter wether asteroid got closer to earth or earth to asteroid), after collision either asteroid has to gain higher momentum or Earth has to gain higher momentum, but not both at the same time. (In reality collision is not the only way to interact - objects can transfer their momentums through light as well).
This asymmetry holds even when both objects have same exact mass, which could be easily demonstrated on a pool table.
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There are actually cases where accelerating reference frames are still invariant: “free fall” would be a good example, in earth-asteroid scenario there is no way to tell wether earth is falling on an asteroid or asteroid is falling on earth as neither spend energy in order to do so. That is why general relativity considers them both locally inertial (before they collide and after they collide, but not at the moment they collide)
Edit: general relativity’s equivalence principle doesn’t work with tidal forces though. Similarly to true inertia, uniform acceleration is just a fiction