Yes most states had state sponsored religions, and all of them got rid of them by the early 1800's. Even considering that, however, the 14th amendment has incorporated the bill of rights and made it applicable to the states.
Also alot of state consitution's were even stricter than the federal consitution about the state and religion, on paper. However when 80% of a state think the same way it is very easy to run roughshod over the other 20%. That is what happened to the catholics when they started to immigrate over here in large numbers during the mid-1800s. When catholics sued the public schools about the use of the KJV of the bible judges in many parts of the US ruled it was alright to use the KJV of the bible AND THAT IT DIDN'T PROMOTE ONE RELIGION OVER ANOTHER.
However anyone with a lick of common sense realizes that it certainly promotes a specific denomination over another. But there was a concertated effort by many in power to try and convert catholics to protestanism. The catholics weren't going for it so they opened their own schools.
Now you have a country that is 76% christian(from the most recent survery I saw) compared to 95% christian at the turn of the century. The best way for the government to be is neutral to religion, neither promoting it nor hindering it.
"Probably ,at the time time of the adoption of the Constitution,and of th eamendment to it,now under consideration(the first),the general if not the universal
sentiment in AMerica was, that Christianity ought to recieve
encouragement from the State,. . ." Joseph Story -"A Familiar Exposition on the Constitution of the United States."from the 1859 original.Corresponds to what was
published in Senate Judiciary Committee Report,1853,second
session, and Corresponding HOuse report following session.
It is my understanding,though I may be wrong, that most
Catholics use the KJV,and it is the most widely used English translation of the Bible?There are serious questions ,yet unresolved concerning the 14th amendment and the wisdom of allowing it to subvert the Bill of Rights and the intent of the men who drafted and ratified the US
Constitution.