dislike and courtesy

It should not be necessary to like someone for you to get along with them well enough to be in community. For you to help them or be helped by them.  There are some very simple courtesies that allow you to interact with the least amount of irritation in spite of vastly differing opinions and view points.
Firstly, you both agree on two solid points:  You will teach each other where your lines are drawn with calm and control. You will not step over a line you have learned exists and you will not feign ignorance of a line you've been taught.  To step over these lines utterly compromises the trust of a relationship that has nothing else on which to build.  We need each other.  Sometimes things go wrong in our lives and we need a community.   If we can't establish even basic trust with each other, how alone are we?
I have a neighbor who has steadfastly rejected me in every possible way, not even deigning to a passing nod or acknowlege my existence.  Today an ambulance made visit to her house.  I struggled with it, but finally chose to go across the street and offer my assistance should she need it.  She dismissed me out of hand.  I have struggled with the ego punch of it all day now.  Balancing that, I've also felt worry and grief for her and her family over it.  I want to get over these things, therefor I will, but right now it's fresh and raw and I'm feeling.  I'm wishing I lived in a world where people agreed to dislike each other and still be a community.  Still support each other through life's worst times. 
Frankly, this state of affairs feels like madness. Perhaps she's mad.  She certainly seems angry.