That is only one possible equilibrium. The other one is that as the sphere of privacy shrinks, people become more and more careful and conformist, until ultimately, everyone is behaving with extreme caution. In this equilibrium, people are locked in a problem of collective action -- nobody dares to say or do what's on his mind, even though most people would like to.

Moreover, even in the "good" equilibrium, the impossibility of hypocrisy protects only those behaviors and opinions that are actually characteristic of a majority. If your opinions and preferences are in a small minority, there is nothing at all to stop you from suffering condemnation, shunning, low status, and perhaps even outright persecution from the overwhelming majority.