Sexuality is definitely socially constructed in many ways. However, it is not socially constructed in all ways.
The link below defines sexuality as
The full range of thoughts and actions that describe sexual motivation and behavior.
When we define sexuality in this way, it becomes clear that sexuality is largely a social construct. For example, both our thoughts and our actions are defined as part of sexuality. Both our thoughts and our actions can be very strongly influenced by the society in which we live.
The Christian faith, for example, teaches us that it is wrong for a man to look at a woman with lust. To the extent that this influences Christians in how they think about sex, it socially constructs their sexuality. Many Christian churches teach that certain kinds of sexual activity, such as sexual activity outside of marriage or sexual activity that cannot lead to conception are illicit. Again, this will strongly “construct” the sexuality of true believers. By contrast, our own society’s more mainstream view that sex is something that regular people should pursue rather uninhibitedly is itself a social construction of sexuality.
Our basic sexual urges are not socially constructed. However, the ways in which we think about those sexual urges and the ways in which we act upon them are socially constructed to a very significant degree.