Jake and PopeBeanie:
The Courts have held that to Establish an institution is to support and subsidize it. So the First Amendment ban on Establishment of Religion would clearly forbid the Federal Government from support and subsidy of religious bodies.
And the Fourteenth Amendment’s first clause makes the restrictions on the Federal Government in The Bill of Rights equally apply to the State Governments also. This clause also makes all natural-born or naturalized Citizens equal before the law, regardless of religion, race, national origin, or other class.
Moreover, no specific religion, whether Abrahamic, Vedic, Pagan, or otherwise, is mentioned in the Constitution, positively or negatively or otherwise. All this means Separation of Religion and State applies even if if the phrase is not explicitly mentioned in the Constitution.