The "power" of promulgating an official religion is not delegated to the United States (in fact, it's specifically prohibited via the Bill of Rights), and therefore, if not prohibited to the states is reserved to the states.
However, the effect of the Fourteenth Amendment is to extend the prohibitions contained in the Bill of Rights to the states as well, under the "equal protection" clause (section 1 : "No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws").
So, prior to 1868, it would have been legal for a state to establish an official religion;it is no longer. Sorry, Outcast.