As additional argument, look at the First Amendment's religion clauses:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof
Notice that the world "religion" is only used once and is shared by the two clauses. Those who argue that the First Amendment only prohibits the government from establishing an official religion, but not from supporting religion non-preferentially, must hold that the same word, in the same sentence, means two entirely different things, since there is universal assent that "religion" for the purpose of the free exercise clause means religion in general, not just a specific religion or denomination.
There's also a caution here regarding construing the Constitution too rigidly based solely on "what it says," as opposed to its actual intent. Notice that the language of the establishment clause is much stronger (or more general, whichever way you look at it) than that of the free exercise clause. Congress is enjoined from legislation "respecting" establishment, that is having anything to do with, or touching upon, the subject. Whereas with respect to free exercise Congress is only enjoined against "prohibiting" it.
Yet no one thinks we should take the "prohibiting" language literally. That is no one thinks that the government is permitted to substantially REGULATE the exercise of religion so long as it stops short of outright "prohibiting" it. And no one thinks or would seriously suggest that there is the slightest need to clarify this point with further amendment.
I think, BTW, that this also supports my previous message. If the authors of the First Amendment believed the Constitution otherwise conferred on the government any powers regarding religion, they never would have used this "prohibiting" language because then it would imply that the national government might regulate religious exercise short of prohibition. It's precisely because the federal government had to power to do anything regarding religion that such semantic details are unimportant.
It's precisely because the federal government hadtono power to do anything regarding religion that such semantic details are unimportant.