1. If your bathroom has a window leading to the outside, there is no need to leave a ventilation fan on the door to prevent bad smells from spreading into the room. In addition, from a Feng Shui perspective (my sister-in-law just told me this, although I don’t believe it myself) the bathroom door should be completely sealed and kept closed when not in use to prevent dirty air from flowing into the room.
2. If your bathroom does not have a window leading to the outside, then you should leave a vent so that ventilation can be provided even with the door closed. After all, health is the most important thing. In this case, you should spray air freshener frequently.