The fourth amendment in the Bill of Rights is where most people see the "right of privacy" in the Constitution. But if you read it, you will see it isn't there.
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
A person cannot, for example, keep slaves in the basement of their homes and argue that this is their right by privacy. The government, upon learning of the infraction, may obtain a warrant and correct the crime.
The provision in the 4th amendment doesn't exempt us from the force of laws that might affect what we do in the privacy of our own homes. It simply ensures the presumption of innocence. This seems like an important distinction.
A lawyer (which I am not) might find my analysis lacking. This is likely. I maintain, however, that law is not just if it cannot be understood by the people who will live under it. I think it is valuable to see how normal citizens view the law so that it can be altered as necessary by normal processes. Thus, I offer my interpretation.