We are not neglecting your opinion. [You are referring to the fact that, at the current moment, you are not neglecting his/her opinion] We do not neglect your opinion = We do not neglect your opinion at any time, now , in the past or in the future. However, it is a clumsy way to say it. Usually one might say "We will never neglect your opinion."

The word "neglect" is unusual with "opinion". We respect the opinions of others, We may disagree with the opinions of others. We may view someone as foolish for holding a specific opinion. There is no way to get "are not" to create a meaningful sentence. We are mindful of the the opinions of others. We are not contemptuous of the opinion of others. Duties can be neglected. Lawns can suffer from neglect.

Instead of the verb "neglect," I would use "ignore" (to not take notice of), "dismiss" (to put aside), or "disregard" (to pay no attention to). 1. (at the moment) We are not disregarding your opinion(s). 2. (in general) We do not disregard your opinions. We value your input highly.