I think you will find that the prevailing interpretation is much broader than a literal reading of the text, in a number of ways. Though it mentions "make no law" it applies to executive agency rulings, though it specifies "Congress" it applies equally to state and local governments, etc.
If you're going to make legal nitpicks, you should probably have a thorough understanding of the jurisprudence.
In my original GP comment above, I was describing actual, recent rulings until the "nuh uh 1st amendment!" comment.
And I wish you were right. That was how I always read it too but we've found out repeatedly - and recently - that state & local governments (and state universities) can ban numerous things, contrary to the 1st Amendment.
I'm not sure what you're talking about, but the first amendment is exactly why state governments and local governments must allow, for example, the local satanic temple to open the council meeting with a prayer. And why publicly funded universities must allow street preachers and pro-life demonstrators.
If you're going to make legal nitpicks, you should probably have a thorough understanding of the jurisprudence.