The green car superstition goes back to 1920, when Gaston Chevrolet, the brother of Chevrolet Motors co-founder Louis Chevrolet, was racing a green car when he was killed in an accident. After that, the color quickly slipped in the popularity rankings (even though British Racing Green has always remained a high-class shade ... for civilian cars, anyway). A lot of pro drivers strongly prefer not to get behind the wheel of a green car, but it's not always up to them.
This superstition brings a logical problem: sponsorships. The entire racing industry, no matter what kind of vehicle, depends on corporate sponsorships, and corporate sponsors want their cars to be in the company's colors. If the car isn't a rolling advertisement for the company, the company isn't getting its money's worth out on the track. And some companies simply chose green, without considering that the color might someday make a race car driver a little nervous. Some brands, such as Skoal and Mountain Dew, sponsored highly successful NASCAR vehicles in the 1980s, which has helped decrease the prevalence of this superstition somewhat. The FedEx Ground car is another, more recent example of a successful green sponsorship in NASCAR. After all, money is green, too. Just as long as we're not talking about $50 bills.