MagiK, the "congress shall make no law" part gets hooked in through two steps. (1)SPENDING -- it was a governmental appropriation that bought the thing, and is therefore a legislative act. (2) 14th Amendment -- makes it clear that any constitutional limit applicable to the federal government will also apply to State governments.
I think the law is clear that, via statues, policies, and other sorts of ways to innundate folks, the government could "establish" religion or "limit the free exercise thereof" without going so far as to found and build a Church of America.
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