The theory behind the Bill of Rights says that our rights exist whether or not the Bill of Rights says we do, or because it is convenient, or because it is logical to your mind. We have them because they are part of our nature as human beings, and the rights in the Bill of Rights confirm that there are certain aspects of our nature as people in which the government has no authority to intervene.
The ability to freely think, speak, associate with others, and move about, or the ability to worship as we please, or not worship at all, involve our sovereignty over our own minds and persons. The government cannot compel moon-landing doubters and conspiracy theorists to disavow their crackpot ideas. Not because the crackpots are necessarily right (sometimes paranoid bastards ARE right, after all), but because our government has no sovereign right to rule our minds. An earlier commenter related the 5th amendment protections as analogous to the 4th interms of search and seizure. I view the 5th amendment's right to not self-incriminate as more like an intersection of the 1st and 4th amendments, because it involves not just our things, but our thoughts. I see it as self-evident that our thoughts are more closely bound to our being, and more deserving of impenetrable legal protection than our effects.
At their root, "Rights" as the Constitution lays them out are an explicit restriction on governmental power. Not the other way around.