Welcome to the garage. First it should not be able to start in gear, only in park or neutral.
Which year jeep and what engine?
Indeed could be park/neutral switch adjustment when it is only influenced by the shift lever position.
But since opening the door seems to have influence as well, just wondering what that could have to do with it. Does it start by only opening the door, or after closing it? The vibration caused by closing the door could do something to the park neutral switch for example.