Danny's got that right! You have to worry not only about animals; but also, people, especially immature people and kids. Last year, I went to a gathering where our tiny trailers were on display. I not only caught people looking through my cabinets but also, someone turned both of the stove's gas burners on full. Luckily, I had turned the tank gas off, on the tongue. Can you imagine if my trailer had one of those new Coleman stoves that is self lighting?!
If you are certain that someone that you trust will be watching, it is probably okay to leave it open...as long as that someone is watching, not sleeping. But, if not, close and lock it. Even if you have someone nearby to watch while you maybe visit the restroom, more than that may be asking too much of a fellow camper or non-family member. Even during the day, at a gathering where strangers may be visiting trailers, I've been told to hide items of value. Small items can develop "legs" and "walk away". One never knows.