Non negotiable things are the deal breakers in a relationship. They are the things you are not willing to compromise on.
When I was single a couple of my non-negotiables would have included: authentic, real relationship with the living God, he would want to have children and would not have been divorced. These would have been deal breakers.
Without question I would have not married someone who was not solid in their walk with the Lord. Who loved God and His Word above all else!
I would not have married someone who did not want to have children (of course the Lord is in control of that, but would have wanted to have the heart for having children). I also would not have married someone who was divorced.
Thinking through this list before you become emotionally involved can be helpful in sorting through your ideas of what you want and what you can work with! I do think this list doesn't have to be a mile long, if so, you may never get married ;-)