If you really think that privacy is unimportant in the 21st century then perhaps you should consider
Consider that Roe v Wade, the landmark Supreme Court decision making abortion legal, was decided on the basis of a right to privacy.
http://en.wikipedia.org/wiki/Roe_v._Wade#Right_to_privacy
The Court declined to adopt the district court's Ninth Amendment rationale, and instead asserted that the "right of privacy, whether it be founded in the Fourteenth Amendment's concept of personal liberty and restrictions upon state action, as we feel it is, or, as the district court determined, in the Ninth Amendment's reservation of rights to the people, is broad enough to encompass a woman's decision whether or not to terminate her pregnancy."
No privacy rights means no abortion rights. Bear in mind as well that corporations such as Target can already often tell when a woman is pregnant from her digital metadata, if corporations can do that then so can government.
Would you trust the NC state legislature to respect a woman's right to privacy in reproductive matters? How about a Republican US Senate and House?