In my experience the key is knowing if the butternut had finished growing. Once they are full size and the skin is still green but hardening then they will keep ripening to some degree once picked and even chnage colour, however if the skin was green but still soft as the butternut was still growing it will not continue to ripen and should be eaten quickly as they will dry out. They are still delicious young too! And i often cut them thinly into stir fries at that stage.
Also for storage green picked butternut won't store as long as those that have fully ripened on the vine.
Ralph