Since the setting of the book is on an uninhabited by other people island, the Robinson family doesn't really have to follow any cultural or social norms that are present in a society that is inhabited with people, however one norm that I liked about the family on the island is that the only food they could eat is what they found, and on the island there was only natural and healthy food which is why they could survive over a period of a very long time on the island.
I think that a social norm on the island that the main character likes is how he is treated by his family because they are very kind and respectful towards him just as they would be if they were not stranded on an uninhabited island. If the children stopped respecting and listening to the main character (their father) then the family would fall apart.
I think that if the main character(s) would be transported to present time they probably wouldn't have used a ship to get to a certain destination but would rather use a plane so there would be a much less chance that they would crash and end up stranded on the island. I think that the main character would find extremely shocking the ways of transportation that we use today.
I think that one social norm from the present (2014) that the main character would enjoy is having cell phones because then they might be able to communicate with other family members on the island or even call someone to rescue them.
One of the social norms present in the book and still present today is treating your family members, especially your parents, with respect and kindness.