This is certainly a point of contention among even those of a libertarian persuasion. Some argue that the Constituion is supposed to be applied directly to the states and cite the 2nd Amendment as an example. In their minds, any state law that somehow infringes upon the right to keep and bear arms is clearly unconstitutional. However, many of them will also turn around and argue that state laws permitting abortion should be considered constitutional, despite the fact that the 14th Amendment prohibits states from passing laws that deprive life without due process.
This would seem to be more of a First Amendment case; a person is being prohibited from referring to the Constitution. But we would then have to address the issue of whether or not the 1st Amendment was written with the states in mind. The language seems clear enough when it says, "Congress shall make no law...abridging the freedom of speech."
Many people hold the position that the 14th Amendment applied the Bill of Rights directly to the States, though I fail to see that exact language. The 14th Amendment essentially re-stated what had already been said in the 5th Amendment, but since the "ratification" of the 14th Amendment the general assumption has been that the Bill of Rights is now suddenly applicable to the states.
As I mentioned before, I am a staunch constitutionalist. I am also a firm believer in states' rights. In short, I'm not entirely 100% sure what my position is on this particular issue. And that's rare!