You don't have to keep both eyes open because for relatively short distances the brain very accurately deciphers distance without using triangulation. You can prove this by estimating distances to a target or object with only one eye open (your dominant eye). You'll most likely find your range estimation is just as good as with both eyes open. Nevertheless, people keep repeating the notion that you won't have good distance judgement. That is simply false.
That said, I have no problem with and slightly recommend both eyes open for instinctive shooters. Hower, if you are gap shooting or consciously using the arrow tip as a sight, one eye closed may be preferred.
Keep in mind not everyone shoots instinctive. In fact, instinctive shooting is way overhyped IMHO. It is the number 1 reason why the majority of bowhunters "fall to pieces" when shooting at real game. They fail to pick a spot. This tendency is hugely reduced by aiming methods. That is not to say aiming methods don't have their own draw backs, they do. However, at close range say 25 yds. and preferably 20 yds. and less, they offer many advantages. Further, they can be adapted with great results out to farther distances.
Aiming methods can also be shot with both eyes open, but in general one eye shut offers superior focus.