I've changed in the car with very little issue. I throw a beach towel over my lap, but if there's no one around, I have done it without the towel. Heck, one time I got drenched in a cold spring rain, before I had rain gear. This was before I lived in Concord, and we had driven here and parked smack in the center of town. DH put the heat on high and I stripped right in the front seat, with just a small towel to dry myself . I was definitely more worried that I had hypothermia.
When my son was racing, there were several racers (guys) who wore changing kilts, so they could stand up and change outside of their cars. They put the kilt on over their shorts, then pulled the shorts down and off, and then put on regular shorts.