See there? There's no need to even snark on that. It's the sort of thing other people might say as parody—an in-character Stephen Colbert could really own that phrase, could stretch it into a whole bit—but the thought leaders of conservatism toss this stuff out like candy. Of course my religion dictates how you should live, you ungodly little tramps of the world. That is why I have my religion. What the hell is the point of any of it if I can't tell you what your "rights" are?
Like religious zealots seizing control of a new Iraqi town, the first order of business for a closely held corporation will be to distribute notes telling the locals which sub-sub flavor of religion they shall be adhering to today. So long as it is about sex, and ensuring it has the proper "consequences," and applies only to women, and I must repeat it must only apply to women, there won't be any problem. Doesn't have to have any science involved, either—if your religion sincerely believes that unmarried women having sex causes tornados to happen, the best legal minds in America will tell you that American law must defer to that crackpot notion. Or any crackpot notion. Or all the crackpot notions, simultaneously, so long as they are explicitly and only about the religious "consequences" of a female American having sex.
You can't parody something that's indistinguishable from a parody in the first place. Of course my religion trumps your scare-quotey "rights," say the ever-angry conservative wags who appear on television and write staggeringly vapid op-eds and perhaps scrawl out a book or two on how the terrible liberals want to control people and dictate to them how they are supposed to live. Why on earth would you think otherwise?