He didn't ignore his grandpa. (Interestingly emotive language on your part, though). He flew in for his grandpa's funeral, visited his granny, and then flew back to his pregnant wife
Harry was given plenty of notice - weeks in fact - to fly home and say a private goodbye to a grandfather he used to be extremely close to. He choose not to, and instead launched the Oprah show instead. Flying back for the funeral is beside the point, he let all of his family down at a moment of great loss. I am not sure that will ever be forgotten or forgiven. Harry only added to their pain at a time of great stress and suffering.
I think that depends on the family and who they're mourning. It also depends on the individual's moral compass, and how the feel about mental health and other issues
You are right, it does depend on a person's moral compass, agreed, and in that department Harry is very much lacking.
There is never a good time to savage your family in public, on a global scale, and anyone with an ounce of decency wouldn't choose to do so in the midst of such mourning. It is callous and insidious.