The human sex drive is innate, but our ideas of sexuality, attractiveness, potency and virility (in the abstract) all seem to be influenced by culture.
Mate selection is at least in part hard-wired. There are criteria that may be impossible to remove. However there seems to be good evidence that ideas of attractiveness/beauty are influenced by culture.
In some parts of the world, it is said that a larger belly is attractive because it represents material success and access to food. This makes the person with the large belly "fit" as a mate because he/she may have resources to offer beneficial to child rearing.
In other places where access to food is less of an issue, a smaller belly is a sign of health and fitness.
I think that sexuality is biological, but people's reactions to it are a sociological and cultural context. This means that if a person is a homosexual, he may be so because of a biological reason, but the actions of the person as gay might be based on cultural expectations.
I believe that sexuality is definitely influenced by society and culture, just as all facets of our lives are influenced by culture. Sexual expectations vary depending on culture, time period, religion, and other factors. Features that are found attractive in one society may be considered bizarre in another society. For instance, small feet on women were considered to be sexually attractive in ancient China, so much to the point where women's feet were being binded in a graphic procedure, so that their feet couldn't grow anymore. Nature and genetics certainly play a major role in sexuality, but so do the time period and culture we are a part of.
Certainly, social expectations and role models play a very significant part in developing an individual's sexuality. It's not the only shaping factor; biology plays an important role, too. However, I suspect that society might be the more important formative force, although I doubt there would be any way to objectively evaluate the actual extent of influence of either nature or nurture in the development of sexuality.
I think sexuality is partly a social construct and partly a biological one. We are biologically programed to seek a mate and reproduce just like other animals. There are certain elements to sexuality that are innate. The hormones and pheromones humans produce are one example. The biological differences between men and women also lead to some innate aspects of sexuality. I think society does influence how we feel about that sexuality. While it is biologically driven, society and culture influence what we think about it and how we respond to our biological impulses.
Inasmuch as other facets of being human are influenced by one's social environment, so is one's sexuality. Does the society go around dictating what one's sexuality should or can be? No, but there is a cultural influence, and a growing acceptance about the choices individuals make regarding their sexuality.
Sexuality is socially constructed to at least some extent.
Obviously, there is a strong biological aspect to sexuality. We are attracted to whoever we are attracted to based largely on our hormones. We cannot really choose (I would argue) who we are attracted to.
However, the way in which we see human sexuality is strongly socially constructed. We in America tend to see sexuality in a very black and white way. We perceive people as being heterosexual or homosexual. We are less likely to understand sexuality as a continuum of attraction. Just as we tend to see people as either "black" or "white" we also tend to see them as either "straight" or "gay." We are not good at understanding sexuality in more nuanced ways, seeing it as a continuum between 100% heterosexuality and 100% homosexuality.