"There is no rain right now, we don't need an umbrella."
没有 is required because of the "There is" part of the sentence. Remember that in addition to "to have" 有 also translates to "there is / there are" . 现在不下雨 is probably closer to "its not raining right now", and while the meaning of the sentence is the same, I think the use of 没有in this sentence is an important distinction. Especially for new learners.
i wrote the same. if 下雨 is a verb we should write 不 because the action is not happening now, 没 is for past actions. maybe i am wrong though