Leaving your car door open can indeed drain the battery, though it depends on a few factors. If your car is newer and has an automatic light sensor that turns the lights off when you close the door, then leaving the door open shouldn't have too much of an effect. However, if your car doesn't have this feature or if the sensor isn't working properly, then the interior lights will stay on and will eventually drain the battery. Additionally, if you leave any other electronic accessories on (like the radio), they will also contribute to draining the battery.
In general, it's not a good idea to leave your car door open for extended periods of time, as it can lead to a dead battery. If you're going to be getting in and out of your car frequently or need to keep the door open for some reason, make sure to turn off any unnecessary electronics so that they don't run down the battery.