Something to read:

U.S. Constitution: First Amendment
RELIGION
An Overview

Madison’s original proposal for a bill of rights provision concerning religion read: ”The civil rights of none shall be abridged on account of religious belief or worship, nor shall any national religion be established, nor shall the full and equal rights of conscience be in any manner, or on any pretence, infringed.”

The language was altered in the House to read: ”Congress shall make no law establishing religion, or to prevent the free exercise thereof, or to infringe the rights of conscience.”

In the Senate, the section adopted read: ”Congress shall make no law establishing articles of faith, or a mode of worship, or prohibiting the free exercise of religion, …” It was in the conference committee of the two bodies, chaired by Madison, that the present language was written with its some what more indefinite ”respecting” phraseology. Debate in Congress lends little assistance in interpreting the religion clauses; Madison’s position, as well as that of Jefferson who influenced him, is fairly clear, but the intent, insofar as there was one, of the others in Congress who voted for the language and those in the States who voted to ratify is subject to speculation.

It’s rather clear. The 1st Amendment is a statement of neutrality regarding religion. They can neither establish a religion or prevent the free exercise of religion. Given that the government cannot establish religion it goes without saying that therefore they cannot engage in the exercise of religion to the point of endorsing any particular religion (or no religion). The main point being, “Congress shall make no law establishing religion.”