A lot depends on what you mean by politically responsible. This brilliant novel does force us to ask ourselves some very hard and harsh questions about the way in which gender and sexuality are constructed entities and yet are so incredibly important to our lives throughout the ages. One of the most fascinating parts of the novel is when Orlando changes from a man to a woman, but then the narrator comments that apart from this minor difference, "in every other respect, she remained precisely as he had been." The text is therefore famous for the way in which it treats sexual identities and gender identities as roles that we take up and adopt like we would put on a new costume.
Of course, we could argue that there is an element of irresponsibility in this. Sociologists would argue that gender is something that, however much we like to treat is as a social construction, is important precisely because of the way in which it involves not just how we view ourselves but how others view us. Many people unfortunately have their life chances substantially reduced precisely because of the way that society views them and fixes their identity because of their gender and sexuality. Unfortunately, the vast majority of us do not have the luxury of changing our identity freely without consequence as our identity is fixed for us by society.