To be and stay in a completely neutral state of mind, would to me indicate to refrain from any emotion. Nothing that is said or done can 'touch' you. You can then clearly respond in a manner you see fit.
But emotion is a big part of being human. Obvious solution is to (learn to) control your emotions, that much is clear. ALso the hardest part, I guess.
What is your view on this?
You must open yourself to others. Not only the ones you like, but even the people you despise. If you want to stay neutral you must be non judgemental, and this is to all. If you are not non judgemental to everyone (no exception), you are not neutral.
You must be able to control your own emotions be acccepting the emotions of others and being able to contain them, without being influenced by them.
This is very difficult while it is the same as removing fear in yourself. Fear is the emotion of nonacceptance. Contracting is fear, and the same thing which happens in your mind when you judge someone in your mind. You close the door and shut them out. It must stay open.