Not necessarily true. Jurisprudence over the 14th Amendment has led to the incorporation doctrine. This doctrine holds that the Bill of Rights applies to state governments as well as the Federal government. Under that doctrine, a state cannot establish an official religion any more than the Federal government can.
You can agree with the incorporation doctrine or not, but it is well established in judicial proceedings and it is not going to be overturned any time soon. The states cannot and will not for the forseeable future have the power to establish an official religion.
I am familiar with the incorporation doctrine that was established by Cantwell v. Connecticut in 1940. This, however, was a false reading of the 14th Amendment. If there was any freedom established by the 1st Amendment it was that of the states to regulate religion. This was an egregious example of legislation by the court. It is also the foundation for the elimination of morals from the law and the resulting hostility toward religion. We should no more accept this as established law as Roe v. Wade or a possible ruling in favor of same sex marriage. The first step in overturning it is to speak the truth about its true meaning.