Does your privacy entitle you to kill? Can your privacy, as a parent, entitle you to beat your children or kill others?
The argument for privacy is an argument for competing rights. It is the State's (note, this means the state, not the Federal Government) responsibility to do the least harm when rights conflict. In this case, not being able to kill your child, born or preborn, along with the right to rape, maiming, torture, or otherwise abuse of children/people is the least harmful intervention of government. As such, privacy is tertiary.
In the end, the right to privacy is dependent upon what you want to do with the privacy. If your privacy harms no other person, then yes; the government has no business being in yours.