This superstition probably goes back to the idea that if you do something once, and it works, you should keep doing it to see if it brings good luck. It's a little odd, though; after all, most drivers enter the car from the designated side, the driver's side. Nico Hulkenberg and Mark Webber are two F1 drivers who believed it was good luck to always climb into the car from the left side. Juan Pablo Montoya is another driver who chooses to enter his cars from the same side every time -- he also buckles his belts exactly the same way, whether he's practicing or competing.
This superstition can also be seen in motorcycle and motocross racing, where racers get a choice of how they prefer to mount the bike. This is another of Valentino Rossi's many rituals, mounting the bike the exact same way every time -- after talking to it, of course.