Actually, you got part of this correct. The Constitution specifically forbade the federal government from interfering in religions, INCLUDING the official state religions. If you check the history, you'll find that the Constitution did NOT prohibit official state religions, and many states had them, long after the Constitution was ratified.
Mark
From what I've read, many more States had them early on, but by the time the Constitution Convention was convened, most had already abandoned them for the same reasons the Founders explicitly excluded them from the federal government. The practice doesn't seemed to have lasted long in the remaing states afterward. It's simply bad practice and doesn't make for good government.