Existentialism encourages people to aim toward radical subjectivity or, in other words, the development of identity separate from social conditions and influence. Radical subjectivity, however, in its purest form, is simply not achievable. The issue is that people can not avoid being influenced by their environment. Our environment is, after all, a leading factor in what differentiates one person from another. Therefore, to a large degree, people act how their environment has shaped them to act. One cannot act separately or distinctly from their environment because their desire for these actions was, in fact, formed by the environment. It seems to me that the pursuit of Radical subjectivity is nothing more than a lost cause.
Now, if you believe that many of the things that most people value, such as family, morality, and relationships, are merely social constructs but also think radical subjectivity is not wise to pursue, you are in a tough spot. What I would recommend is just embracing the social constructs despite your lack of belief in them. This is no small task, but I believe the conditions of life will be better for everyone if you embrace the systems. I am not saying you have to always agree with the majority of people, but maybe attempt to buy into a few values that many people would claim to have meaning and you personally feel drawn to. This is at least a more desirable path to take than radical subjectivity. I will not go in depth but radical subjectivity would lead to some morally dark areas, especially if everyone attempted to pursue it. So as counter-intuitive as it may seem, participating in the systems of society is your best bet.