How to use audio signal from car speaker as transistor switching signal?
Car radios can have bridged output stages for more output power with 12VDC voltage. The speaker output signal is not at all a voltage against ground. You should use a transformer or optocoupler as isolating element.
You can connect one optocoupler (=the led side) with series resistor in parallel with the speaker. The optocoupler output side feeds base current to the transistor which gives DC to the led stripe. Use 2 optocouplers by connecting the outputs in parallel and the inputs too, but leds to opposite directions to have drive from plus and minus halves of the speaker signal.
DO NOT skip proper calculations or you can pull the smoke out as well from the radio and the leds and their wiring and driver.
Something to think:

It's possible that you want some smoothing to prevent too sharp led flicker. Designing the drive with proper decay time constant is totally a new problem.
Any extra electronics in a car is a new possibility to have failures. Making a device which does not disintegrate in car's vibrations is anything but trivial.
I wouldn't accept disco lights in a car except in case the car is parked.