Inaccurate reporting/editorializing alert. A factually accurate account would read as follows:
The Constitution bars any act of congress regarding an "establishment" of religion.
Read Art VI.. Our Constitution and its Amendments are the Law of the Land, any State laws "to the Contrary notwithstanding".
States cannot infringe upon our rights to life, liberty, or property by respecting the 'establishments' of religions in the due process of making law. [see the 14th]
If you want to argue that including a display of the 10 Commandments constitutes an establishment of a state religion, then you are on very shaky ground. But to use the 14th amendment to argue that such a recognition somehow "abridges the privileges or immunities of citizens" or "deprives any person of life liberty or property" then you are really stretching to find some basic liberty to never be offended by seeing a religious display in public. Sorry but that is not a constitutional right.
What privilege or immunity do you think is being abridged if a state court or a city hall "endorses" a particular religion by displaying the 10 commandments or even a scripture verse? What liberty are you being deprived of? This notion of somehow extending the imaginary wall of separation between church and state out to even the most local of government institutions has led courts to curtail the freedom of speech and freedom of religious exercise to students across the country.