I think what he means is that while things such as natural laws affect us all the same, a very large part of our lives as individuals is that we have different views on what is important, how to relate to the world around us, and how to relate to other people.
It isn't so much that reality is different, but that our perception of it is definitely subjective. And in many field (not much in science, but much in politics, for example) our subjective view is what makes us function as humans.